DE102007017254B4 - Device for coding and decoding - Google Patents

Abstract

An apparatus for encoding a sequence of samples of an audio signal, with each sample within the sequence having an original position, includes a sorter for sorting the samples depending on their sizes, in order to obtain a sorted sequence of samples, with each sample having a sorting position within the sorted sequence. Furthermore, the apparatus has an encoder for encoding the sorted samples and information on a relation between the original and sorting positions of the samples.

Description

The The present invention relates to a device and a Method for coding and decoding information signals, as they occur, for example, in the audio and video encoding can.

at The coding and decoding of information signals are in the range the conventional technique so-called lossy coding known. For example, transformation-based ones already exist Coding method, such as MPEG 1/2 Layer-3 (MPEG = Moving Picture Expert Group, MP3) or Advanced Audio Coding (AAC). These work with a time-frequency transformation and a psychoacoustic model, which perceptible signal components of non-perceivable signal components can differentiate. The subsequent quantization of the data in the frequency domain is controlled with these models. It stands, however for the coded signals only a small amount of data available, so z. B. a low overall bit rate can be met, is a coarser Quantization the result, d. H. caused by the quantization then clearly perceptible coding artifacts.

In The conventional technique is also the parametric coding method known, such as Philips Parametric Coding, HILN (HILN Harmonic and Individual Lines and Noise), etc., which are the original ones Synthesize the signal on the decoder side. At low bit rates arises thereby a falsification of original sound characteristics., d. H. such coding methods can then show noticeable differences to the original.

in the In the field of lossless coding, there are basically two different ones Approaches. The first method supports to predict the time signal. The resulting predictor error is then subsequently entropy-coded and comes to storage or transmission.

The second method uses a time-frequency transformation as the first processing step with following lossy coding of the resulting spectrum. In addition, can then the one in the reverse transformation resulting errors are entropy-coded to a lossless coding to ensure the signal z. B. LTAC (Lossless Transform Audio Compression).

It There are also two basic ones options for data reduction. The first possibility corresponds to a redundancy reduction. Here is an uneven probability distribution exploited an underlying alphabet of the signal. symbols, the one higher Appearance probability, z. With fewer bits represented as symbols with a smaller probability of occurrence. Often this principle is also called entropy coding. At the Encode / decode process, no data is lost. A perfect one (lossless) reconstruction of the data is again possible. The second possibility an irrelevance reduction. In this type of data reduction will be for the User selectively removes non-relevant information. As a basis be for this often models of natural perception restrictions used by the human senses. In the case of audio encoding is used a psychoacoustic consideration of the input signals as a perceptual model, which then controls a quantization of the data in the frequency domain. Since data is selectively removed from the encoding / decoding process, a perfect reconstruction of the data is no longer possible. It is therefore a lossy data reduction.

At usual Transformation based audio coding methods become the input data transformed from the time into the frequency domain and there with Help of a psychoacoustic model quantized. Ideally This quantization only causes so much quantization noise inserted in the signal, that this for the listener is imperceptible, but this is not respected for low bit rates can be - it clearly audible Kodierartefakte. Furthermore, it is often at low target bit rates necessary a downsampling with previous low pass filtering, so then is a transmission high frequency components of the original Signal no longer possible without further notice. Claim these processing steps a considerable computing power and bring a limitation of signal quality with himself.

Ziya Arnavut describes coding concepts based on permutations, including index permutations, in his dissertation "Permutation Techniques in Lossless Compression", Lincoln, Nebraska, September 1995. The font concentrates primarily on lossless image compression, such as the JPG (JPG = Joint Various coding concepts are examined and compared on the basis of the coding costs, ie the required data bits per coded symbol, which discloses approaches which proceed from a sorting of the data to be compressed, such as a sorting of a data sequence consisting of 8 Bit greyscale values of a grayscale image of the exist.

A. A. Babaev "Procedures of Encoding and Decoding of Permutation ", in: Plenum Publishing Corporation, UDC 519.15: 681.3, pp. 861-863, 1985, describes a concept for permutation coding. Much combinatorial and assignment problems are based on filling in an optimal objective function or permutation coding. The document discloses methods for Permutationscodierung.

Raad, M., et al. "Audio coding using sorted sinusoidal parameters ", in: IEEE Circuits and Systems, 2001, ISCAS 2001, p. 401-404, vol. 2 discloses a concept for encoding audio data that based on sinusoidal signals.

sinusoidale Coding allows the representation of audio signals by means of sums of harmonics, d. H. sinusoidal signals. An efficient coding can be achieved at the parameters, d. H. Amplitudes, phases and frequencies that are harmonic transmitted, where at Decoder by overlaying the individual sub-signals, the original signal to be reconstructed can. The document further discloses the parameters of a basic function to sort, for example, based on their performance or energy or their psychoacoustic significance. Depending on the desired Code rate can then starting with the most significant parameters, more or less Transfer data become.

The DE 102 30 809 A1 discloses a method of transmitting audio signals between a transmitter and at least one receiver according to the method of prioritizing pixel transmission. First, the audio signal is decomposed into a number of spectral components. The decomposed audio signal is stored in a two-dimensional array with a plurality of fields, with frequency and time as dimensions, and the amplitude as each value to be entered in the field. Then groups are formed from each individual field and at least two fields of the array adjacent to one another in this field, and a priority is assigned to the individual groups, the priority of a group being selected the greater the amplitudes of the group values are and / or the larger the amplitude differences the values of a group and / or the closer the group is to the current time. Finally, the groups are transmitted to the recipient in order of priority.

The The object of the present invention is thus to provide an alternative Concept for coding and decoding of information signals create.

These Task is solved by a coding device according to one of claims 1, 22, 43, 61, a Vorrich device for decoding according to any one of claims 12, 33, 53, 66, a method of coding according to one of claims 10, 31, 51, 64, a method for decoding according to one of claims 20, 41, 59, 69.

Of the The present invention is based on the finding that an information signal expenses cheaper can be encoded if a sorting is performed before. It can be assumed that an information signal or else an audio signal comprises a sequence of samples, wherein the Samples from a time or frequency signal, d. H. it can also be a sampled spectrum. The term sample is thus not meant to be limiting. In exemplary embodiments Therefore, the present invention can be a fundamental processing step consist in the sorting of an input signal according to its Perform amplitude, this also take place after any pre-processing has taken place can. As preprocessing could in the field of audio signals, for example, a time / frequency transformation, a prediction or a multi-channel redundancy reduction, z. In multi-channel signals, generally, also decorrelation methods. Before these processing steps can additionally still a possible variable division of the signal into defined periods, so-called frames, take place. Also a further division of this Time periods in subframes, which are then sorted individually, is possible.

In embodiments After the sorting step, on the one hand, the sorted data exist and secondly, a sorting rule, which is present as a permutation of the indices of the original input values. Both records then be possible effectively coded. embodiments offer several options, such as a prediction with following Entropy coding of the residual signal, d. H. determining prediction coefficients for a prediction and determining the residual signal as a difference between a Output signal of the prediction filter and the input signal.

In other embodiments, a curve fit with appropriate Funktionsvorschrif th and function coefficients with subsequent Entropiekodierung the residual signal. In other embodiments, a lossy coding can take place and thus the coding of the residual signal also omitted.

embodiments can also perform a permutation coding, for example by creation of inversion tables and subsequent entropy coding.

In other embodiments can also be a prediction of inversion tables and subsequent entropy coding of the Rest signal passed through be, as well as a prediction the permutation and subsequent Entropy coding of the residual signal. Embodiments can by Omitting the residual signal also achieve lossy coding. Alternatively, you can create numbering for the permutations take place, cf. A.A. Babaev: Procedures of encoding and decoding of permutations, Kibernetika, no. 6, 1984, pp. 77-82. Further can combinatorial selection method with subsequent numbering in exemplary embodiments be used.

preferred embodiments The present invention will be described below with reference to FIG the enclosed drawings closer explained. Show it:

1a an embodiment of a device for coding;

1b an embodiment of a device for decoding;

2a an embodiment of a device for coding;

2 B an embodiment of a device for decoding;

3a an embodiment of a device for coding;

3b an embodiment of a device for decoding;

4a an embodiment of a device for coding;

4b an embodiment of a device for decoding;

5 Exemplary embodiments of an audio signal, a permutation and an inversion panel;

6 an embodiment of an encoder;

7 an embodiment of a decoder;

8th another embodiment of an encoder;

9 another embodiment of a decoder;

10a an example of a frequency spectrum with approximation of an audio signal;

10b an example of a sorted frequency spectrum and its approximation of an audio signal;

11 an illustration to illustrate a sorted-lossless encoding;

12 an example of a sorted difference-coded signal and its residual signal;

13 Example of a sorted time signal;

14 an example of sorted time values and a corresponding curve fitting; and

15 a comparison of the coding efficiency of differential coding and curve fitting.

16 exemplary processing steps of most lossless audio compression algorithms;

17 an embodiment of a structure of a prediction coding;

18 an embodiment of a structure of a reconstruction in a prediction coding;

19 an embodiment of warmup values of a prediction filter;

20 an embodiment of a predictive model;

21 a block diagram of a structure of a LTAC encoder;

22 a block diagram of an MPEG-4 SLS encoder;

23 a stereo-redundancy reduction after decorrelation of single channels;

24 a stereo-redundancy reduction before decorrelation of single channels;

25 an illustration of the relationship between predictor order and total bit consumption;

26 an illustration of the relationship between quantization parameter g and total bit consumption;

27 an illustration of a magnitude frequency response of a fixed predictor as a function of its order p;

28 an illustration of the relationship between permutation length, number of transpositions and codability measure;

29 a representation of inversion tables in the 10th block (frame) of a noise-like piece;

30 a representation of inversion tables in the 20th block (frame) of a tonal piece;

31 a representation of a permutation of a noise-like piece in the 10th block (left) and a tonal piece (right) created from a sorting of time values;

32 on the left a part of an audio signal, the corresponding permutation and inversion table LS, and on the right the permutation and the inversion table LS from the left picture enlarged;

33 on the left a part of an audio signal, the corresponding permutation and inversion table LS, and on the right the permutation and the inversion table LS from the left picture enlarged;

34 a probability distribution (above) and a length of the codewords (below) of a predicted (Fixed Predictor) residual signal of an inversion table LB;

35 a probability distribution (above) and a length of codewords of a difference signal-generated residual signal (below) of sorted time values;

36 a percentage of a partial block decomposition with a least amount of data of a forward adaptive Rice coding over a residual signal of a fixed predictor of a piece including side information for parameters, the total block length is 1024 time values;

37 a percentage of a subblock decomposition with the least amount of data of a forward adaptive Golomb coding over the residual signal of a fixed predictor of a piece including side information for parameters, the total block length is 1024 time values;

38 an illustration of the operation of a history buffer;

39 an illustration of the operation of an adaptation compared with an optimal parameter for the entire block;

40 an embodiment of a forward-adaptive arithmetic coding with assistance me a backward adaptive Rice coding;

41 a representation of the influence of the block size on the compression factor F;

42 a representation for lossless MS encoding;

43 another illustration for lossless MS encoding; and

44 an illustration to select a best variant for stereo reduction reduction.

Regarding the following description should be noted that in the different embodiments identical or functionally identical functional elements same reference numerals and thus the descriptions of these functional elements in the various embodiments illustrated below interchangeable. It is also on it again pointed out that in the following embodiments representative for discreet Values of a signal is generally spoken of samples. The term sample is not intended to be limiting, samples can by sampling a time signal, a spectrum, a general one Information signal, etc. may have arisen.

1a shows a device 100 for encoding a sequence of samples of an audio signal, each sample having an origin position within the sequence. The device 100 includes a device 110 for sorting the samples by size (after any preprocessing, eg, time / frequency transformation, prediction, etc.) to obtain a sorted sequence of samples, each sample having a sorting position within the sorted sequence having. Furthermore, the device 100 An institution 120 for encoding the sorted samples and information about a relationship between the original and sort positions of the samples.

The device 100 may further comprise a preprocessing means configured to perform a filtering, a time / frequency transform, a prediction or a multi-channel redundancy reduction for generating the sequence of samples. In embodiments, the device 120 for encoding to encode the information about the relationship between the source and sort positions as index permutation. Optionally, the device 120 for encoding, encode the information about the relationship between the source and sort positions as an inversion chart. The device 120 The coding may further be adapted to the sorted samples or the information. encode the relationship between the source and sort positions with differential and subsequent entropy coding or only one entropy coding.

In other embodiments, the device may 120 determine and encode coefficients of a prediction filter based on the sorted samples, a permutation or an inversion table. In this case, furthermore, a residual signal which corresponds to a difference between the sampled values and an output signal of the prediction filter can be coded and enable lossless coding. The residual signal can be coded with an entropy coding. In a further embodiment, the device 100 a device for setting function coefficients of a functional specification for adaptation at least to a subregion of the sorted sequence and the device 120 for encoding may be formed to encode the function coefficients.

1b shows an embodiment of a device 150 for decoding a sequence of samples of an audio signal, each sample having an origin position within the sequence. The device 150 includes a device 160 for receiving a sequence of coded samples, each coded sample having a sorting position within the sequence of coded samples, and the device 160 is further adapted to receive information about a relationship between the original and sort positions of the samples. The device 150 also has a device 170 for decoding the samples and the information about the relationship between the source and sort positions, and further comprising means 180 for resorting the samples based on the information on the relationship between the source and sort positions so that each sample has its original position.

In embodiments, the device 160 for receiving to receive the information about the relationship between the originating and sorting positions as an index permutation. Furthermore, the device 160 for receiving to receive the information about the relationship between the originating and sorting positions as an inversion chart. The device 170 For decoding purposes, embodiments may be configured to decode the encoded samples or the information on the relationship between the source and sort positions with entropy and subsequent difference decoding, or only entropy decoding. The device 160 For receiving, optionally coded coefficients of a prediction filter can be received and the device 170 for decoding may be configured to decode the coded coefficients, wherein the device 150 and further comprising means for predicting samples or relationships between the source and sort positions based on the coefficients.

In further embodiments, the device 160 for receiving, to further receive a residual signal corresponding to a difference between the samples and an output of the prediction filter, and the means 170 for decoding may further be configured to adjust the samples based on the residual signal. The device 170 can optionally decode the residual signal with an entropy decoding. The device 160 for receiving could also receive function coefficients of a functional specification and the device 150 could further comprise means for adapting a functional rule to at least a portion of the sorted sequence and the device 170 for decoding could be designed to decode the function coefficients.

2a shows an embodiment of a device 200 for encoding a sequence of samples of an information signal, each sample having an origin position within the sequence. The device 200 includes a device 210 for sorting the samples by their size to obtain a sorted sequence of samples, each sample having a sorting position within the sorted sequence. The device 200 also includes a device 220 for setting functional coefficients of a functional specification for adaptation to at least one subregion of the sorted sequence and a device 230 for coding the function coefficients, the samples outside the sub-range, and information about a relationship between the original and sort positions of the samples.

The device 200 may further comprise a preprocessing means configured to perform a filtering, a time / frequency transform, a prediction or a multi-channel redundancy reduction for generating the sequence of samples. In embodiments, the information signal may include an audio signal. The device 230 For encoding, it may be configured to encode the information about the relationship between the originating and sorting positions as an index permutation. Furthermore, the device 230 be adapted to encode to encode the information about the relationship between the original and sorting positions as Inversionstafel. Optionally, the device 220 also be configured for coding to encode the sorted samples, the information about the relationship between the original and sorting positions with a difference and then the entropy coding or only an entropy coding. The device 230 The coding could also be designed to determine and to code coefficients of a prediction filter based on the samples, a permutation or an inversion table.

In further embodiments, the device 230 for encoding, further configured to encode a residual signal corresponding to a difference between the samples and an output of a prediction filter. The device 230 for encoding, in turn, may be adapted to encode the residual signal with entropy coding.

2 B shows an embodiment of a device 250 for decoding a sequence of samples of an information signal, each sample having an origin position within the sequence. The device 250 includes a device 260 for receiving coded function coefficients, sorted samples, and information about a relationship between a sort position and the origin position of samples. The device 250 also includes a device 270 for decoding samples and means 280 for approximating samples based on the function coefficients at least in a portion of the sequence. The device 250 also has a device 290 for resorting the samples and the approximated portion based on the information about the relationship between the original and sort positions so that each sample has its original position.

In embodiments, the information signal may include an audio signal. The device 260 for receiving, it may be arranged to receive the information about the relationship between the originating and sorting positions as an index permutation. Furthermore, the device 260 for receiving, the information about the relationship between the originating and sorting positions to receive as an inversion table. The device 270 Optionally, it may decode the sorted samples or the information about the relationship between the source and sort positions with entropy and then difference decoding or only entropy decoding. The device 260 for receiving may further be adapted to receive coded coefficients of a prediction filter and the device 270 for decoding may be configured to decode the coded coefficients, wherein the device 250 and further comprising means for predicting samples based on the coefficients.

In further embodiments, the device 260 for receiving, a residual signal representing a difference between the samples and an output signal of the prediction filter or the device 280 for approximating corresponds to receive and the device 270 for decoding may be configured to adjust the samples based on the residual signal. The device 270 For decoding, optionally, the residual signal may be decoded with entropy decoding.

3a shows a device 300 for encoding a sequence of samples of an information signal, each sample having an origin position within the sequence. The device 300 includes a device 310 for sorting the samples by their size to obtain a sorted sequence of samples, each sample having a sorting position within the sorted sequence. The device 300 also includes a device 320 for generating a sequence of numbers depending on a relationship between the original and sort positions of the samples and for determining coefficients of a prediction filter based on the sequence of numbers. The device 300 also has a Einrich device 330 for encoding the sorted samples and the coefficients.

The device 300 may further comprise a preprocessing means configured to perform a filtering, a time / frequency transform, a prediction or a multi-channel redundancy reduction for generating the sequence of samples. In embodiments, the information signal may comprise an audio signal. The device 320 for generating the sequence of numbers may be formed to generate an index permutation. Optionally, the device 320 To generate the sequence of numbers, create an inversion table. The device 320 for generating the sequence of numbers may be adapted to further generate a residual signal corresponding to a difference between the sequence of numbers and a prediction order predicted on the basis of the coefficients. The device 330 for encoding may be adapted to encode the sorted samples according to difference and subsequent entropy coding or only one entropy coding. The device 330 for encoding may further be configured to encode the residual signal.

3b shows an embodiment of a device 350 for decoding a sequence of samples of an information signal, each sample having an origin position within the sequence. The device 350 includes a device 360 for receiving coefficients of a prediction filter and a sequence of samples, each sample having a sorting position. The device further comprises a device 370 for predicting a sequence of numbers based on the coefficients and a device 380 for reordering the sequence of samples based on the sequence of numbers so that each sample has its original position.

In embodiments, the information signal may comprise an audio signal. Furthermore, the device 370 to predicate the sequence of numbers an index permutation as a number sequence predicate. The device 370 Predicting the sequence of numbers could also predict an inversion chart as a sequence of numbers. The device 360 for receiving may further be configured to receive a coded residual signal and the device 370 for prediction can be designed to take into account the residual signal in the prediction of the sequence of numbers. The device 350 may further comprise means for decoding configured to decode samples following entropy and subsequent difference decoding or only entropy decoding.

4a shows an embodiment of a device 400 for encoding a sequence of samples, each sample having an origin position within the sequence. The device 400 includes a device 410 for sorting the samples by their size to obtain a sorted sequence of samples, each sample having a sorting position within the sorted sequence. The device 400 also includes a device 420 for encoding the sorted samples and encoding a sequence of numbers having information about the relationship between the source and sort positions of the samples, each element unique within the sequence of numbers, and wherein the means 420 for coding assigns a number of bits to an element of the sequence of numbers, the number of bits allocated to a first element is greater than the number of bits allocated to a second element if fewer elements were already coded before the coding of the first element than before the coding of the second element.

wobei die unten geöffneten Klammern anzeigen, dass der Wert in den Klammern auf die nächstgrößere ganze Zahl aufgerundet wird.The device 420 The coding may be designed to encode a number sequence of length N and to code a number of X elements simultaneously, the number of X elements being assigned to G bits according to FIG

the brackets below show that the value in parentheses is rounded up to the next larger integer.

In another embodiment, the device 420 be designed to encode to encode a number sequence of length N, where X is a number of already encoded elements of the sequence of numbers, where the next element of the sequence of numbers G bits are assigned according to, G = ⌈log 2 (N - X) ⌉ with 0 ≤ X <N.

4b shows an embodiment of a device 450 for decoding a sequence of samples, each sample having an origin position within the sequence. The device 450 includes a device 460 for receiving a coded sequence of numbers and a sequence of samples, each sample having a sorting position. The device 450 also includes a device 470 for decoding a decoded number sequence having information about a relationship between the source and sort positions based on the encoded sequence of numbers, each element unique within the decoded sequence of numbers, and the device 470 for decoding assigns a number of bits to an element of the number sequence such that the number of bits allocated to a first element is greater than the number of bits allocated to a second element if less prior to the decoding of the first element Elements were already decoded, as before the coding of the second element. The device 450 also includes a device 480 for reordering the sequence of samples based on the decoded number sequence such that each sample within the decoded sequence has its original position.

In embodiments, the device 470 for decoding to decode a number sequence of length N and to simultaneously decode a number of X elements, wherein the number of X elements are assigned to G bits according to,

The device 470 for decoding may further be configured to decode a sequence of numbers of length N, where X is a number of already encoded elements of the sequence of numbers, which are assigned to the next element of the sequence of numbers G bits according to, G = ⌈log 2 (N - X) ⌉ with 0 ≤ X <N.

The 5 shows on the left side waveforms of an audio signal 505 (large amplitudes), a permutation 510 (mean amplitudes) and an inversion chart 515 (small amplitudes). On the right side are the permutation 510 and the inversion panel 515 for a better overview again shown in a different scale.

From the in the 5 shown gradients, can be a correlation between the audio signal 505 , the permutation 510 and the inversion panel 515 detect. The correlation transfer of the input signal to the permutation or inversion chart can be clearly recognized. According to embodiments, in addition to a coding of the sorted samples, a permutation coding can take place by creating inversion tables, which are subsequently entropy-coded. From the 5 It can be seen that due to the correlations also a prediction of the permutation or the inversion tables is possible, whereby the respective residual signal can be entropy coded, for example, in the case of a lossless coding.

The prediction is possible because a correlation present in the input signal is transferred to the resulting permutation or inversion table, cf. 5 , As prediction filters known FIR (FIR = Finite Impulse Response) and IIR (IIR = Infinite Impulse Response) structures can be used. The coefficients of such a filter are then selected so that, for example based on a residual signal at the input of the filter, at its output the original output signal is present or can be output. The corresponding coefficients of the filter and the residual signal can then be transmitted more cost-effectively, ie with fewer bits or transmission rate than the original signal itself. In a receiver, or a decoder then the original signal, based on the transmitted coefficients and optionally a residual signal predicted or reconstructed. The number of coefficients or the order of the prediction filter determines, on the one hand, the bits necessary for transmission and, on the other hand, the accuracy with which the original signal can be predicted or reconstructed.

at The inversion tables are an equivalent representation of the Permutation, however, for an entropy coding are more suitable. For lossy coding is it equally possible that resort only incomplete perform, thus save on data traffic.

The 6 shows an embodiment of an encoder 600 , In the encoder 600 can be a preprocessing 605 the input data (eg time / frequency transformation, prediction, stereo-redundancy reduction, band-limiting filtering, etc.). The preprocessed data is then sorted 610 , where sorted data and a permutation arise. The sorted data can then be further processed or coded 615 For example, here can be a difference coding. The data can then be entropy-coded afterwards 620 and a bit multiplexer 625 to provide. The permutation can also be processed or coded first 630 , For example, by determining an inversion table with possibly subsequent prediction, whereupon an entropy coding 635 can be done before the entropy-coded permutation or Inversionstafel the bit multiplexer 625 fed. The bit multiplexer 625 then multiplexes the entropy-coded data and the permutation into a bitstream.

The 7 shows an embodiment of a decoder 700 for example, a bit stream according to the encoder 600 receives. The bitstream is then first in a bitstream demultiplexer 705 demultiplexed, whereupon encoded data is entropy-decoded 710 be supplied. The entropy-coded data can then be used in a decoding of the sorted data 715 , z. B. in a differential decoding continue to be decoded. The decoded sorted data is then resorted 720 fed. From the bit stream multiplexer 705 Furthermore, the coded permutation data of an Entropiedekodierung 725 fed, which further decoding the permutation 730 can be downstream. The decoded permutation will then also be resorted 720 fed. The resort 720 may then output the output data based on the decoded permutation data and the decoded sorted data.

embodiments can further having a coding system having 3 modes of operation. One Mode 1 could be high compression rates using a psychoacoustic approach enable the input signal. A mode 2 could be Medium compression rates without psychoacoustics and a mode 3 could be lower Compression rates, but with lossless coding allow.

All modes in common could be the waiver of the processing stages of quantization, resampling and low-pass filtering. It could thus be transmitted in all 3 levels, the full bandwidth of the input signal. 8th shows a further embodiment of an encoder 800 , 8th shows the block diagram of an encoder 800 or a coding method for modes 1 and 2. The input signal is by means of a time-frequency transformation 805 , z. B. an MDCT (MDCT = Modified Discrete Cosine Transform) transformed into the frequency domain.

Thereafter, the spectral lines are sorted according to the magnitude of their amplitudes 810 (Sorting). Since the resulting sorted spectrum has a relatively simple curve shape, in embodiments it can easily be approximated by a function rule by means of a curve fit 815 (Curve Fitting) ,. In order to be able to bring the permutation of the spectral line indices on the decoder side, which had resulted from the resorting, back into the original order, and thus to be able to restore the original spectrum, a re-sorting rule can now be used 820 be found and written to the bitstream, which includes the smallest possible amount of data. This can be for mode 1, for example, by run-length coding 820 and for mode 2 through a special permutation encoder 820 be accomplished, which can work with the help of an inversion board.

The data of the run length coding or of the permutation coder 820 are then additionally by an entropy coding or entropy coder 830 coded and finally including some additional information, eg. B. the coefficient of the above-mentioned functional rule written in the bit stream, indicated by the bitstream formatter 835 , Possibilities to control the arising data volume (variable bitrates) exist eg. In the variation of the quality of the curve fitting, by the optional addition of a psychoacoustic observation in a psychoacoustic model 840 of the input signal as well as by different coding strategies of the permutation coder 820 or the run-length coding 820 , This shows the 8th also a block 825 which monitors the bitrate generated in the coding process and, if necessary, provides feedback to the psychoacoustic model if the data rate is still too high.

The block diagram of 8th this shows a psychoacoustic model 840 for bitrate control, this can for example be activated only for the mode 1 and in mode 2 can be dispensed with this control option in favor of coding quality. In operation mode 1, a higher compression rate is achieved than in the other two operating modes. This is done with the help of a psychoacoustic analysis 840 Of the input signal, targeted lines of the frequency spectrum are set to zero or, alternatively, elements of the index permutation excluded from resorting to the transmission of the resort rule 820 To save data. In contrast, in operating mode 2, the frequency spectrum is completely restored, there are only small errors due to small inaccuracies of the curve approximation 815 on. Furthermore, the operating mode 2 can be extended with the addition of a residual signal to a lossless mode. Both in mode 1 and mode 2, the entire frequency spectrum can be transmitted, ie the data reduction in mode 1 can only by a reduced Rücksortiervorschrift 820 be achieved.

The 9 shows a further embodiment of a decoder 900 or a decoding process of the modes 1 and 2 essentially the steps of coding or encoder 800 goes backwards. The bitstream is first passed through a bitstream demultiplexer 905 unzipped and in an entropy decoder 910 decoded. From the decoded function coefficients of a function specification can then by an "Inverse Curve Fitting" -Block, ie an inverse curve fitting 915 the function or spectral function are restored and a rescaler 920 be supplied. The recycler 920 also obtains a permutation from a permutation decoder 925 which decodes the permutation based on the entropy-coded permutation. The recycler 920 can then use the permutation and the spectral function rebuilt with the aid of the transferred function coefficients to bring their spectral lines into their original order. Finally, the reconstructed spectrum is transformed by an inverse transformation 930 , z. Inverse MDCT, transformed back into the time domain.

In other embodiments can also apply to the time / frequency transformation be omitted and an information signal directly in the time domain sorted as described above, coded and transmitted.

The 10a shows an example of a frequency spectrum of an audio signal with 1024 frequency lines and its approximated spectrum, where original and approximation are almost identical. 10b shows the associated sorted spectrum and its approximation. It is clear that the sorted spectrum can be more easily and accurately approximated by a functional specification than the original spectrum. To the spectrum 10b to approximate, it may be in embodiments in z. B. 5 areas (partitions or English partitions) are divided, which in the 10b are shown, wherein the area 3 z. B. by a straight line and the areas 2 and 4 with correspondingly suitable functions (eg, polynomials, exponential functions, etc.) are approximated. The number of amplitude values in the areas 1 and 5 can be chosen very small in embodiments, z. B. 3, but since these are enormously important for the sound quality, they should either be very accurately approximated or transmitted directly.

Thus, according to exemplary embodiments, only the function types and their coefficients or, for the ranges 1 and 5, if necessary, the amplitude values can be transmitted for the entire spectrum. The selected division into 5 areas is only an example, it is of course always possible to choose other divisions to z. B. to improve the quality of the approximation. 10a shows in addition the approximated and sorted back spectrum, where it is easy to see that the reconstructed spectrum comes very close to the original spectrum.

In embodiments, the resorting results in a number sequence of the spectral line indices, which represents a permutation of the index quantity. In embodiments, the number sequence of these resorted indexes can be transmitted directly, whereby relatively large amounts of data can arise, which, since they are completely uniform, can not be reduced by an entropy coding. To the gleichverteilte Zahlenfol In the case of the indices of the sorted spectral lines, this sequence of numbers is logically unsorted to map to an unequally distributed sequence, in embodiments an inversion table formation can be applied to the indices, which represents a bijective, that is to say unambiguously reversible, mapping and an unequally distributed result.

An invariably distributed inverted number sequence is now entropy-coded and thus the data volume to be transmitted is reduced. The following is a small example of how the inversion panel works. Given a set of number pairs A = {(xi, y _1), ..., (x _n, y _n) where the x _i are intended to provide indexing of y _i, so that the x _i form a monotonically strictly increasing sequence , The y _i could be z. B. be amplitude values of a frequency spectrum, z. B. A = ((1, 5), (2, 3), (3, 1), (4, 2), (5, 8), (6, 2.3), (7, 2), (8, 4.5), (9, 6)}.

Now, A is sorted on the basis of the size of y _i , so that the y _{i form} a monotone decreasing sequence. The x _i thus become an unsorted number sequence, ie a permutation of the original x _i .
A '= ((5, 8), (9, 6), (1, 5), (8, 4.5), (2, 3), (6, 2.3), (4, 2), (7, 2 ), (3, 1))
x _i '= {5, 9, 1, 8, 2, 6, 4, 7, 3}
y _i '= {8, 6, 5, 4.5, 3, 2.3, 2, 2, 1}

Inversion table formation of x _i : x _i ' 5 9 1 8th 2 6 4 7 3 (Equally distributed) x _i ' ^-1 2 3 6 4 0 2 2 1 0 (not equally distributed)

The inversion of the inversion table returns the original sequence of numbers: x ₉ ' ^-1 = 0 9 x ₈ ' ^-1 = 1 9 8th x ₇ ' ^-1 = 2 9 8th 7 x ₆ ' ^-1 = 2 9 8th 6 7 x ₅ ' ^-1 = 0 5 9 8th 6 7 x ₄ ' ^-1 = 4 5 9 8th 6 4 7 x ₃ ' ^-1 = 6 5 9 8th 6 4 7 3 x ₂ ' ^-1 = 3 5 9 8th 2 6 4 7 3 x ₁ ' ^-1 = 2 5 9 1 8th 2 6 4 7 3 = x _i '

in principle There are other possibilities the inversion table formation possible, see, for. B.

Ziya Arnavut: Permutations Techniques in Lossless Compression, Dissertation, 1995th

Farther would be in other embodiments after the formation of the inversion chart, a difference coding like them z. In Ziya Arnavut: Permutation Techniques in Lossless Compression, Dissertation, 1995, or other post-processing (eg prediction), which reduce the entropy, conceivable.

embodiments The present invention operates on a completely different principle than already existing systems. By avoiding the calculation steps of Quantization, resampling and low-pass filtering and by the optional renouncement of a psychoacoustic consideration may be exemplary embodiments at computational complexity save on. The quality the coding depends for the Mode 2 exclusively of kindness the approximation of the functional specification to the sorted frequency spectrum, while for the Mode 1 the quality mainly determined by the psychoacoustic model used.

The bitrate of all modes depends for the most part on the complexity of the resort rule to be transferred. The bit rate scalability is given in a wide range, from high compression to lossless coding at higher data rates, any gradation is possible. Due to the principle of operation, the full frequency bandwidth of the signal can be transmitted even at relatively low bit rates. The low demands on the computing power and the memory space allow an application and implementation of embodiments not only on conventional PCs, but also on portable terminals.

Furthermore, z. As an application in the field of MPEG-4 Scalable, MPEG Surround,
or in the low-delay range, possibly also in conjunction with an application in the time domain possible.

There the functional principle of embodiments does not impose restrictive requirements on the signal to be coded, can Also, applications in particular of loss-free mode outside audio encoding, such as in video encoding or other areas.

There the resulting bit rates are significantly different from the complexity of the ones to be transmitted Resort regulation depend, are still other embodiments conceivable. An improvement is possible for example, when transferring a key becomes, on the decoder side, the resulting permutation clearly identifiable. Existing work in the field of "Restricted Permutations" can be found here as a basis.

embodiments can additionally the transfer provide an error or residual signal, hereby could quality Modes 1 and 2 increased, the mode 2 even to a lossless Fashion to be extended. Furthermore, a transmitted error signal could be a intelligent rearrangement for the in mode 1 from resort allow excluded frequency lines, and so the quality of this Continue to improve the mode.

embodiments can for the Mode 1 also provide a synthesization of frequency lines similar to SBR (SBR = Spectral Band Replication) works, but not exclusively for the upper one Frequency domain responsible is, but deleted Intermediate frequency areas reconstructed. Also a special on the in the approximation resulting errors tuned psychoacoustic Consideration could in further embodiments the quality increase and lower the bitrate. Because the principle of resorting and subsequent Curve approximation does not rely on signals from the frequency domain is, can other embodiments also in the time domain for be used in the mode 2. Since the modes 2 and 3 on the use can dispense with a psychoacoustic consideration, embodiments also outside the audio encoding are used.

embodiments can and one adapted to the specificities of this procedure provide optimized processing of stereo signals and thus can the bit consumption and the computational effort compared to a double mono encoding reduce again.

Exemplary embodiments make use of a sorting model. In a coding method working according to the sorting model, a sorting of the data to be coded takes place. As a result, on the one hand, an artificial correlation of the data is brought about, which makes the data easier to encode. On the other hand, the sorting results in a permutation of the original positions of the time values. In order for a decoder to be able to reconstruct an original information or audio signal, it is thus necessary to encode and transmit a reordering rule (permutation) in addition to the coded time values. As a result, the original problem of merely encoding the time values is now broken down into two subproblems, that is to say a coding of the sorted time values and a coding of the sorting rule. 11 illustrates the scheme of a so-called "sorted-lossless" coding, for example, an audio signal is mapped to a signal with stronger correlation, and then the sorted time values and a sorting rule are coded.

From the basis of the 11 The principle described is also derived from the name SOLO (SOLO = Sorted Lossless) for the novel lossless coding method or audio coding method. Each of the two subproblems has very special properties. For the coding of the sorted time values offers in embodiments z. B. a difference coding. The coding of the permutation can z. In the equivalent inversion panel display. The following section deals in detail with the two subproblems. In addition to the sorting model, traditional decorrelation methods, such as predictive modeling, can be used in SOLO.

• 1. Blockeinteilung (Frameing)
• 2. Dekorrelation der unsortierten/sortierten Zeitwerte
• 3. Verarbeitung der Permutation
• 4. Entropiekodierung der Daten aus 2. und 3.

In the case of the Sorting Model, an additional processing step, the processing of the permutation, is added compared to conventional coding methods. Thus, in embodiments, for example, four basic processing steps result:

• 1. Blocking (Frameing)
• 2. Decorrelation of unsorted / sorted time values
• 3. Processing of the permutation
• 4. entropy coding of the data from 2. and 3.

at The difference coding, as the name says, is not the actual one Value, but encodes the difference of successive values. If the differences are smaller than the original values may be higher compression be achieved.

Let i ∈ N (N = set of natural numbers) with 1 ≤ i ≤ n <∞ and x _i ∈ Z (Z = set of integers), then the difference coding can be defined as:

The difference coding is invertible. Let i ∈ N (N = set of natural numbers) with 1 ≤ i ≤ n <∞ and x _i ∈ Z (Z = set of integers), then the inverse difference coding can be defined as:

There difference coding is a simple way of prediction is also a warmup (a time value at i = 1) of excluded from the entropy coding. 6 has the property that when descending sorted time values complete the rest signal in the amount of positive natural Numbers lies. By doing so leaves make a subsequent Entropiekodierung easier. A Difference coding works optimally when the ones to be coded Values are very close to each other, so are highly correlated. By sorting the time values, the time values become one strong correlation.

12 shows an exemplary course of a difference-coded sorted signal and its residual signal, ie

12 shows the effect of difference coding applied to sorted time values. The matching value of sorted and decorrelated time signal at index 1 (warm-up or warm-up phase) can be clearly recognized.

Furthermore, the much smaller dynamic range of the residual signal of the difference coding compared to the sorted time values is striking. Detailed information to 12 are to be taken from the following table. The difference coding thus represents a simple and efficient method for coding sorted time values. Max. Value (without warmup) minute value Warmup Sorted time values 32425 -32768 32767 Residual signal δ 2630 0 32767

Curve fitting (CF = Curve Fitting) is a technique that attempts in exemplary embodiments to adapt a given mathematical model function as best as possible to data points, in this case the sorted time values. The effectiveness of curve fitting is essentially determined by the shape of the curves to be described. What is certain is that, depending on the type of sorting, it is a monotonously decreasing or monotonically increasing waveform. The 12 and 13 show two representative waveforms of sorted time values. Noteworthy is the uneven waveform in 13 , Such curves, which occur in about 40% (related to a selection of different audio signals) of the cases, can usually not be described very well by a Curve Fitting.

To curves as in the 12 and 13 shown to approximate, the following function is selected. This function proved to be well suited in experiments to describe the waveforms available here.

The coefficients c ₁ , c ₂ , λ ₁ , λ ₂ are elements of the set of real numbers and can, for. B. with the Nelder-Mead Simplex algorithm.

This algorithm is a method for optimizing nonlinear functions of multiple parameters. Similar to the Regula-falsi method with step size control, the tendency of the values towards the optimum is approximated. The Nelder-Mead Simplex algorithm converges roughly linearly and is relatively simple and robust. The function f _cf1 has the advantage that it can adapt very flexibly to a whole series of curves. The disadvantage, however, is that relatively much page information (four coefficients) is needed. It is also noticeable that parts of the sorted curves, z. B. the middle section of 12 , could be well described by a polynomial of first degree (straight line) and only two real coefficients a, b would be needed. Therefore, a second function should alternatively be used: f cf2 (x) = αx + b.

A curve fit over the total number of sorted time values of a block is certainly too inaccurate. Therefore, it would be useful to divide the block into several smaller partitions. But if you decompose the block into too many partitions, which are described by the functions f _cf1 and f _cf2 , you need a lot of function _coefficients . Therefore, in one embodiment, for a fixed total block length of 1024 Time values subdivide into 4 partitions each 256 Time values made. In order to be able to decide per partition whether f _cf1 or f _{cf2 is} better suited for curve fitting, an adequate decision _criterion is required. The decision criterion should be easy to identify and meaningful. In order to ensure this, the residual signal of the respective function is initially formed and an estimate of the bit requirement is made. Since function f _{cf1 requires} twice as many coefficients as f _cf2 , an additional 32 bits are estimated for f _cf1 .

In 14 the operation of Curve-Fitting is shown. In this frame, the first and fourth partitions are described by fcf2 and the second and third partitions are written by fcf1.

Finally, a direct comparison between the difference coding and a decorrelation by curve fitting is made. For this, the respective costs are specified in bytes per frame. In order to ensure a direct comparison of both coding methods, a forward adaptive Rice coding with only one parameter is used in both cases. In all blocks, the difference coding performs better than the curve fitting or curve fitting specified here, a comparison is in 15 shown.

In the following, details of embodiments of the present invention will be explained in more detail. The following table lists the audio material used in the following, which is referred to in corresponding places. No. filename sampling rate bit channels annotation source style 1 adia m.wav 44100 Hz 16 1 k. A. pop 2 White m.wav 44100 Hz 16 1 OdBFS se White noise 3 es01 m.wav 44100 Hz 16 1 Suzanne Vega k. A. pop 4 es02 m.wav 44100 Hz 16 1 sliced SQAM German Male 5 es03 m.wav 44100 Hz 16 1 sliced SQAM English Female 6 si01 m.wav 44100 Hz 16 1 sliced SQAM Harpsichord 7 si02 m.wav 44100 Hz 16 1 sliced SQAM Castagnets 8th si03 m.wav 44100 Hz 16 1 k. A. Pitch pipe 9 sm01 m.wav 44100 Hz 16 1 k. A. Bagpipe 10 sm02 m.wav 44100 Hz 16 1 k. A. chimes 11 sm03 m.wav 44100 Hz 16 1 k. A. Dulzimer 12 sc01 m.wav 44100 Hz 16 1 sliced SQAM Trumpet Concerto 13 sc02 m.wav 44100 Hz 16 1 Richard Wagner k. A. Meistersinger 14 sc03 m.wav 44100 Hz 16 1 k. A. pop 15 sine1k Hz OdB.wav 44100 Hz 16 1 OdBFS se 1k Hz sine wave 16 adia LegR.wav 44100 Hz 16 2 L = R se pop 17 adia.wav 44100 Hz 16 2 k. A. pop 18 es01.wav 44100 Hz 16 2 Suzanne Vega k. A. pop 19 es02.wav 44100 Hz 16 2 sliced SQAM German Male 20 es03.wav 44100 Hz 16 2 sliced SQAM English Female 21 si01.wav 44100 Hz 16 2 sliced SQAM Harpsichord 22 si02.wav 44100 Hz 16 2 sliced SQAM Castagnets 23 si03.wav 44100 Hz 16 2 k. A. Pitch pipe 24 sm01.wav 44100 Hz 16 2 k. A. Bagpipe 25 sm02.wav 44100 Hz 16 2 sliced SQAM chimes 26 sm03.wav 44100 Hz 16 2 k. A. Dulzimer 27 sc01.wav 44100 Hz 16 2 sliced SQAM Trumpet Concerto 28 sc02.wav 44100 Hz 16 2 Richard Wagner k. A. Meistersinger 29 sc03.wav 44100 Hz 16 2 k. A. pop

you can roughly divide the lossless coding into two areas. There are universal procedures that vary with data Can work kind of and there are specialized procedures that are optimized for it very special data such. B. to compress audio signals.

Already For many years, universal methods such as GZIP or ZIP for the compression of digital data. GZIP used for compression the deflate algorithm, which is a combination of LZ77 and Huffman Coding is. Also, the ZIP file format uses a similar one Algorithm for compression. Another universal procedure is BZIP2. Before the actual coding of the data takes place here a precoding with the Burrows-Wheeler transformation (BWT) instead.

BZIP2 also uses a Huffman encoding. These programs can be used on any data such. As text, program code, audio signals, etc. apply. However, due to their mode of operation, these methods achieve much better compression in text than in audio. A direct comparison of GZIP and the SHORTEN compression method specializing in audio signals confirms this, see the following table. The default settings were used for the test. Stucco no. File size (bytes) GZIP file size. F SHORT file size. N F 13 2246022 1962100 1145 1102557 2037 14 2037842 1724447 1182 1304845 1562 17 1912876 1753719 1091 1117413 1712

In order to obtain a good compression factor for audio signals, the special properties of audio signals during compression must be taken into account. Most lossless audio encoding methods have that in 16 shown block diagram together.

16 Fig. 10 exemplifies processing steps of most lossless audio compression algorithms. The presentation in the 16 shows a block diagram, wherein the audio signal is first a block formation or a engl.

"Framing" block is supplied, the audio signal in signal blocks divided. Subsequently, an intra-channel decorrelation block decorrels or engl. "Intra Channel Decorrelation "block single the signal, for example by a differential encoding. In an entropy coding block or engl. "Entropy Coding" block becomes the signal after all entropy.

First, be the data to be processed into signal sections (frames) x (n) ∈ Z (Z corresponds the set of integers) of a certain size. Then follows Decorrelation step in which is tried as well as possible the Remove redundancy from the signal. Ultimately, that will be from the Decorrelation step generated signal e (n) ∈ z entropy-coded. So far There are two principal approaches to the decorrelation step. Most lossless audio coding methods use some sort linear prediction, to remove the redundancy from the signal (predictive modeling). Other lossless audio encoder methods are based on a lossy one Audio coding method, in which besides the lossy data additionally the residual or error signal (even residual signal) to the original signal is coded (Lossy Coding Model). Subsequently, the different Approaches will be considered in more detail.

Linear Predictive Coding (LPC) is widely used in digital speech signal processing. Their importance lies not only in the high efficiency, but also in the relatively low computational complexity. The basic idea of the prediction is to predict a value x (n) from previous values x (n - 1), x (n - 2), ..., x (n - p). If p preceding values are used for prediction, this is called a pth order predictor. The prediction coding methods used in lossless audio coding usually have the in 12 shown basic structure. A ^ (z) and B ^ (z) stand for z-transformation polynomials with quantized coefficients α ^ _k and b ^ _k . Q stands for quantization to the same word length as x (n). The z-transformation is the discrete-time analogue to the Laplace transform of continuous-time signals.

17 shows an embodiment of a structure of a prediction coding. In principle shows 17 an IIR filter structure with a feedforward branch with filter coefficients A ^ (z), a negative feedback branch with filter coefficients B ^ (z), and a quantization Q.

Behind 17 hides the equation

If the prediction coding method works optimally, much of the redundancy is removed from x (n) and represented by the coefficients of A ^ (z) and B ^ (z). The resulting residual signal e (n) is then uncorrelated and significantly smaller in amplitude than the original signal x (n). This achieves a coding gain. If B ^ (z) ≠ 0, ie the feedback term is 0, we speak of an FIR predictor. Otherwise, B ^ (z) ≠ 0, one speaks of an IIR predictor. IIR predictors will not be considered here. IIR predictors are much more complex, but in some cases they can achieve a better coding gain than FIR pedagogues. In order to be able to reconstruct the original signal from the residual signal e (n) and the predictor coefficients, we proceed as in 18 in front.

18 shows an embodiment of a structure of a reconstruction in a prediction coding. 18 shows an embodiment as an IIR filter structure with a Mitkopplungszweig with filter coefficients B ^ (z), a negative feedback branch with filter coefficients A ^ (z), and a quantization Q.

Behind 18 hides the equation

The predictor coefficients are redetermined and transmitted each time for each signal portion to be processed. In this case, the adaptive determination of the coefficients ak of a p-th order predictor can take place either with the covariance method or with the autocorrelation method which uses the autocorrelation function. The autocorrelation method obtains the coefficients by solving a linear system of equations of the following form:

Where _rxx (k) = E (s (n) s (n + k)). Alternatively, this can be done in matrix notation r = Rα represent. Because R is invertible, the coefficients are obtained α = R -1 r

As to be precise on the linear system of equations for the determination of the optimum predictor comes is described in detail in. The equation can be due to the matrix properties of R very effective with the Levinson Durbin Solve the algorithm.

For a prediction one makes a division of the time values into blocks of size N. Assuming one would like to use a second-order predictor to predict the time values from the current block n, then the problem arises as to how to deal with the first two values from block n. One can either use the last two values from the previous block n-1 to predicate them or not predicate the first two values of block n and leave them in their original form. If values from a preceding block n-1 are used, block n is only decodable if block n-1 was successfully decoded. However, this would lead to block dependencies and treat the principle of talking each block (frame) as a stand-alone decodable unit. If the first p values are left in their original form, they will be called engl. Warm-up or warm-up values (see 19 ) of the predictor. Because the warmup usually has different size ratios and statistical properties than the residual signal, it is usually not entropy-coded.

19 shows an embodiment of warmup values of a prediction filter. In the upper area of the 19 unchanged input signals are shown, in the lower area are shown warm-up values and a residual signal.

Another possibility for realizing a prediction is not to re-determine the coefficients for each signal section, but always to use fixed predictor coefficients. Will always Using the same coefficients, it is also called a fixed predictor.

By way of example, AudioPaK, a representative of predictive modeling, will be considered a little closer. First, AudioPaK splits the audio signal into independent decodable sections. Typically, multiples of 192 samples (192, 576, 1152, 2304, 4608) are used. For decorrelation, a FIR predictor with fixed integer coefficients is used (fixed predictor). This FIR predictor was first used in SHORTEN. Internally, the Fixed Predictor has four different predictive models. x ^ 0 (n) = 0 x ^ 1 (n) = x (n - 1) x ^ 2 (n) = 2x (n-1) -x (n-2) x ^ 3 (n) = 3x (n-1) - 3x (n-2) + x (n-3)

In principle, the equation is polynomial approximation or prediction methods. By a polynomial of degree p-1, the preceding p samples x (n-1), x (n-2), ..., x (n-p) can be described. If one now evaluates this polynomial at the position n, one obtains the predicted value x ^ (n). Graphically, you can feel like this 20 to illustrate. 20 shows an embodiment of a predictive model, in a polynomial predictor.

The residual signals e _p (n) = x (n) -x ^ (n) resulting from the prediction can be calculated relatively simply recursively, as in the following equation. e 0 (n) = x (n) e 1 (n) = e 0 (n) - e 0 (n - 1) e 2 (n) = e 1 (n) - e 1 (n - 1) e 3 (n) = e 2 (n) - e 2 (n - 1)

Finally, the best predictive model is determined by making the sum of the amounts of the residual signal values smallest. AudioPaK uses a Rice coding. Since the values of the residual signal e _i (n) ∈ Z, but the Rice coding works with values from N ₀ , a mapping of the residual values e _i (n) to N _{0 is first} made.

The Rice parameter k is determined per block (frame) and assumes values 0, 1, ..., (b - 1). Where b represents the number of bits per audio sample. k is determined by the following equation k = | log 2 (E (| e i (N) |))

A simple estimate of k without any floating-point operations can be done, for example, as follows:
for (k = 0, N = framesize; N <AbsError; k ++, N ^* = 2) (NULL;)

In which framesize the number of samples per frame and AbsError the Represents the sum of the absolute values of the residual signal. Other representatives of Predictive Modeling are SHORTEN, FLAC (see Coalson, Josh: FLAC - Free Lossless Audio Codec; http://flac.sourceforge.net), MPEG-4 audio Lossless Coding (MPEG-4 ALS) and Monkey's Audio (see Ashland, Matthew T .: Monkey's Audio - a fast and powerful lossless audio compressor; http://www.monkeysaudio.com/index.html).

The second way to implement a lossless audio coding method is to set up a lossy audio coding method. A representative of the Lossy Coding Model is LTAC, where instead of LTAC (Lossless Transform Audio Compression) the abbreviation LTC (Lossless Transform Coding) ver is used. The principal mode of operation of the encoder is in 21 shown.

21 shows a block diagram of a structure of a LTAC (Lossless Transform Coding) encoder. The encoder comprises a "DCT" block to transform an input signal x (n) into the frequency domain, followed by quantization Q. The quantized signal c (n) can then be transformed back into the time domain via an "IDCT" block where it can then be subtracted, quantized by another quantizer Q, from the original input signal. The residual signal e (n) can then be transmitted entropy-coded. The quantized signal c (n) can also be determined by an entropy coding, which corresponds to the 21 from different codebooks can be coded.

at LTAC, the time values x (n) by an orthogonal transformation (DCT - Discrete Cosine transformation) transformed into the frequency domain. in the lossy part then the spectral values are quantized c (k) and entropy-coded.

Around Now to realize a lossless coding method, are additionally the quantized spectral values c (k) with the inverse transformation (IDCT = Inverse Discrete Cosine Transformation) and again quantized y (n). The residual signal is represented by e (n) = x (n) - y (n) calculated. Subsequently e (n) is entropy-coded and transmitted. In the decoder you can choose from c (k) through the IDCT with subsequent quantization get y (n) again. Ultimately, a perfect reconstruction of x (n) in the decoder by y (n) + e (n) = y (n) + [x (n) -y (n)] = x (n) realized.

Another method which falls into the category of the Lossy Coding Model is MPEG-4 Scalable Lossless Audio Coding (MPEG-4 SLS). It combines lossless audio encoding, lossy audio coding and scalable audio coding functionality. MPEG-4 SLS is backward compatible at bitstream level to MPEG-4 Advanced Audio Coding (MPEG-4 AAC). 22 shows a block diagram of a MPEG-4 SLS (Scalable Lossless Audio Coding) encoder.

The Audio will be first with an IntMDCT (Integer Modified Discrete Cosine Transform) into the Frequency domain transformed and then by a temporal noise Shaping (TNS) and a center / side channel coding (Integer AAC Tools / Customization). Everything encoded by the AAC encoder is then calculated from the IntMDCT spectral values by an error mapping away. Remains a residual signal which is subjected to entropy coding. For the Entropy coding is a BPGC (Bit-Plane Golomb Co-de), CBAC (Context-Based Arithmetic Code) and Low Energy Mode / Low Energy Mode.

The sound transmission over two or more channels is called stereophony. In practice, the term stereo is usually used exclusively for two-channel pieces. If there are more than two channels, this is called multi-channel sound. This master thesis is limited to signals with two channels, for which the term stereo signals is used synonymously. One way to handle stereo signals is to encode both channels independently. In this case we speak of independent stereo coding (Independent Stereo Coding). Apart from "pseudo-stereo" versions of old mono recordings (both channels identical) or two-channel sound in television (independent channels), stereo signals usually have both differences and similarities (redundancy) between the two channels. If you can identify the similarities and transfer them only once for both channels, you can reduce the bit rate. In this case, one speaks of dependent stereo coding (Joint Stereo Coding). One way to reduce the redundancy between stereo signals is the center / side channel coding (MS coding). How to generate a center channel M and a side channel S from a left channel L and a right channel R shows the following equation

ist die MS-Kodierung invertierbarThere

the MS coding is invertible

Even lossless audio coding methods use the MS coding. However, since the above equation has the property of yielding floating point numbers rather than integers in some cases, some lossless audio coding techniques (see Ashland, Matthew T .: Monkey's Audio - a fast and powerful lossless audio compressor; www.monkeysaudio.com/index.html) uses the following equation for MS encoding M = NINT ( L + R 2 ) S = L - R

NINT here means rounding to the nearest one Integer relative Zero.

In addition to MS coding, lossless audio coding methods also use LS coding or RS coding (see Coalson, Josh: FLAC - Free Lossless Audio Codec, http://flac.sourceforge.net). In order to obtain the right channel from an LS coding or the left channel from an RS coding, one proceeds as in the following equation L = R + S R = L - S

There are two principal ways to perform stereo redundancy reduction (SRR). Either after the decorrelation of the individual channels (see 23 ) or before the decorrelation of the individual channels (see 24 ). 23 shows a stereo-redundancy reduction (SRR) after decorrelation of single channels, 24 a stereo-redundancy reduction before decorrelation of single channels. Both methods have specific advantages as well as disadvantages. In the following, but only method 2 be used.

In this section a suitable quantization is to be developed for the presented linear prediction coding (LPC). The determined coefficients a _z are usually floating-point values (real numbers), which can only be represented with finite precision in digital systems. So there must be a quantization of the coefficients a _z . However, this can lead to larger prediction errors and has to be considered in the generation of the residual signal. Therefore, it makes sense to control the quantization via an accuracy parameter g. If g is large, finer quantization of the coefficients takes place and more bits are needed for the coefficients. If g is small, a coarser quantization of the coefficients takes place and fewer bits are needed for the coefficients. In order to be able to realize a quantization, the largest coefficient a _max is initially determined α = max (| a i |) for j = 1, 2, ..., p.

The thus determined maximum predictor coefficient a _max is now decomposed into a mantissa M and an exponent E to the base 2, ie α = 2 e · M.

The mantissa M is no longer needed in the further course, but the exponent E is used to determine the scaling factor s by the following equation s = g - E - 1.

The subtraction of 1 serves to take account of signed coefficients. The quantized predictor coefficients result for i = 1, 2,..., P by the equation α ^ i = ⌊Α i · 2 s ⌋.

With the scaling factor s and the quantized predictor coefficients α ^ _i , the residual signal e (n) to be transmitted is determined

The equation ensures that e (n) ∈ Z. By a transfer of the warmup, the parameters g, s, p, α ^ _i and the residual signal e (n) to the decoder, a perfect reconstruction of the original values x (n) of this signal section is possible

Enlarged the order of the predictor, this usually reduces the variance and amplitude of the residual signal. This results in a smaller data rate for the residual signal. On the other hand, it is the case that more coefficients are needed for a larger predictor order and a bigger warmup, So more page information, transfer must become. This increases the overall data rate again. The task So it is to find an order in which the total data rate is minimized.

In 25 the relationship between predictor order and total bit consumption is shown. It will be appreciated that as the order increases, the residual signal will require fewer and fewer bits for encoding. However, the data rate for the page information (quantized predictor coefficients and warmup) increases continuously, causing the overall data rate to rise again at some point. As a rule, a minimum is reached at 1 <p <16. In 25 results in an optimal order at p = 5. For 25 a fixed value was used for the quantization control of g = 12 and a resolution of 16 bits per sample for the input signal.

26 shows an illustration of the relationship between quantization parameter g and total bit consumption. If one considers the total data rate as a function of the quantization parameter g (see 26 ), the bit consumption for the residual signal decreases continuously up to a certain value. From here, a further increase in quantization accuracy is of no use. Ie. the necessary number of bits for the residual signal remains approximately constant. The overall data rate initially decreases continuously, but then increases again due to increasing page information for the quantized predictor coefficients. In most cases, the optimum is 5 <g <15 26 the minimum is at g = 11 26 For example, a constant predictor order of p = 7 and a resolution of 16 bits per sample were used for the input signal.

The newly gained insights should now be used to specify an algorithm for lossless linear prediction in a simplified MATLAB code representation (see lpc ()). MATLAB is a commercial mathematical software designed for matrices calculations. Hence the name MATrix LABoratory. Programming is done under MATLAB in a proprietary, platform-independent programming language, which is interpreted on the respective computer. First, some variables after the in 25 and 26 initialized determined limit values. Then the predictor coefficients are determined via the autocorrelation and the Levinson-Durbin algorithm. The core of the algorithm is formed by two nested for loops. The outer loop passes over the predictor order p. The inner loop passes over the quantization parameter g. Within the inner loop, the quantization of the coefficients, the calculation of the residual signal and an entropy coding of the residual signal take place. Instead of a complete entropy coding of the residual signal, an estimate of the bit consumption which might possibly be carried out faster would also be conceivable. Finally, you secure the variant with the lowest bit consumption. Following is an embodiment of a MATLAB code:

Here we will investigate if the FIR predictor with fixed and integer coefficients (Fixed Predictor) described above can be profitably extended. From the above section we know that an optimal order p is in the range of 1 <p <16. The Fixed Predictor uses a maximum order of p = 3. The transfer function of the Fixed Predictor is H (z) = (1 - z -1 ) p , and the magnitude frequency response is H (e jωT ) = | 2 · sin (ωT / 2) | p ,

T here denotes the sampling rate and ω = 2πf. The transfer function is a mathematical description of the behavior of a linear, time-invariant system that has an input and an output. The frequency response describes the behavior of a linear time-invariant system, comparing the output with the input and recording it as a function of frequency. With the aid of the above equation, two further orders p = 4 and p = 5 are designed: x ^ 0 (n) = 0 x ^ 1 (n) = x (n - 1) x ^ 2 (n) = 2x (n-1) -x (n-2) x ^ 3 (n) = 3x (n-1) - 3x (n-2) + x (n-3) x ^ 4 (n) = 4x (n-1) -6x (n-2) + 4x (n-3) -x (n-4) x ^ 5 (n) = 5x (n-1) -10x (n-2) + 10x (n-3) -5x (n-4) + x (n-5)

The corresponding residual signals are given by the following equation and the formation of the warmup is equivalent to the above section: e 0 (n) = x (n) e 1 (n) = e 0 (n) - e 0 (n - 1) e 2 (n) = e 1 (n) - e 1 (n - 1) e 3 (n) = e 2 (n) - e 2 (n - 1) e 4 (n) = e 3 (n) - e 3 (n - 1) e 5 (n) = e 4 (n) - e 4 (n - 1)

27 shows an illustration of a magnitude frequency response of a fixed predictor as a function of its order p. The effect of the different predictor orders becomes clear on the basis of a consideration of their frequency response (see 27 ). With an order of p = 0, the residual signal corresponds to the input signal. This results in a magnitude frequency response of constant 1. Increasing the order leads on the one hand to a greater attenuation of the low-frequency signal components, but on the other hand to an increase in the high-frequency signal components. The frequency axis was normalized for the representation at half the sampling frequency, resulting in 1 at half the sampling frequency (here 22.05 kHz).

A Investigation will now show whether the addition of p = 4 and p = 5 a coding gain can be achieved. This will be different music examined and the block selected the least bits per block needed.

The following table shows how often which order was selected as the best, summed over the entire audio file. For the creation of this table, a constant block length of 1024 time values was taken. Piece no. p = 0 p = 1 p = 2 p = 3 p = 4 p = 5 Total number of blocks 1 0 14 316 67 57 0 454 4 15 69 161 79 0 0 324 6 5 173 115 27 0 0 320 7 3 74 189 43 0 0 309 8th 0 221 959 0 0 0 1180 14 2 30 279 158 4 0 473 15 0 0 0 0 0 216 216

Out The above table shows that there is no predictor order there, in all cases optimal. That's why it makes sense to have the best order for everyone Redetermine block. Most frequently the orders p = 2, p = 3 and p = 1 are selected. Fewer often the orders p = 0 and p = 4 are used. At piece number 1 becomes a coding gain by expanding the Fixed Predictor by p = 4 achieved. The order p = 5 brings a coding gain only at piece 15. There it is by piece Number 15 is not a "normal" music signal, but by a 1 kHz sine, the utility of p = 5 is questionable. In addition, this also indicates that p> 5 usually no large coding gain brings more and only increases the complexity. As in the previous section, The newly gained insights should be used to create an algorithm (see fixed ()). First, the maximum and minimum Order set. Then follows a for loop, which over all Orders running. Within this loop, the residual signal with the corresponding Bit consumption and the cost of the warmup depending on determined by the order. Ultimately, the best option is chosen.

at The difference coding, as the name says, is not the actual one Value, but encodes the difference of successive values. If the differences are smaller than the original values may be higher compression be achieved. The Fixed Predictor described in the previous section used for p = 1 a difference coding.

Definition (difference coding): Let i ε N with 1 <i <n <∞ and x _i ∈ Z, then the difference coding is defined as:

The difference coding is invertible. Definition (inverse difference coding): Let i ε N with 1 <i <n <∞ and x _i ∈ Z, then the inverse difference coding is defined as:

As with the predictors, warmup (a time value at i = 1) is excluded from entropy coding. 6 has the property that with decreasing time values, the residual signal is completely in N ₀ . This makes a subsequent entropy coding easier. Difference coding works optimally if the values to be coded are very close to each other, ie strongly correlated. Sorting the time values places the time values in a strong correlation. 12 already showed the effect of difference coding applied to sorted time values. The matching value of sorted and decorrelated time signal at index 1 (warmup) can be clearly seen. Furthermore, the much smaller dynamic range of the residual signal of the difference coding compared to the sorted time values is striking. Detailed information to 12 are given in the following table. The difference coding thus represents a simple and efficient method for coding sorted time values. Piece No. 2 Max. Value (without warmup) minute value Warmup Sorted time values 32425 -32768 32767 Residual signal δ 2630 0 32767

The following two sections develop methods for effectively coding permutations. Assuming a memory-free consideration of a permutation, then the entropy of any permutation σ is given by | σ | <∞ is given by the following equation. The memory-sensitive consideration of a permutation should be deliberately avoided here, since a memory-free view is the simplest way of coding a permutation H (σ) = log 2 (| Σ |).

H (σ) describes then the necessary Number of bits / characters for binary encoding a σ (i). To z. B. a permutation of the length 256 is needed one per element 8 bits.

This is because the occurrence of the elements of permutation is likely. The permutation resulting from the coding of an audio signal (eg 16-bit resolution) by sorting the time values would in this example alone require half the input data rate. Since this data volume is already relatively high, the following question arises: Can permutations with less than log ₂ (| σ |) bits per element be binary coded?

In the previous section it was shown that one can switch from the permutation representation to an equivalent inversion table representation and back. It is therefore to be investigated whether a binary representation of the inversion chart requires a smaller data rate than that of the permutation. An example should provide information about it. Example: Given are the following permutations

If the inversion table is formed by σ and π, then I (σ) = (2110), I (π) = (3210). It applies H (I (σ)) = 1.5 bits <2 bits = H (σ).

Ie. the entropy of the inversion table is actually smaller than that of the permutation. But for π arises H (I (π)) = 2 bits = H (π).

In the case of π, the entropy of the inversion table is the same as that of the permutation. But considering π in reverse order, ie π (4), π (3), π (2), π (1) gives the identical permutation and its inversion table has a very small entropy. In any case, for any permutation σ with | σ | <∞: H (I (σ)) ≤H (σ).

It Now further inversion panel formation rules are to be defined to counteract the problem with π described in the above example. First should be the completeness half again the inversion boarding instruction described in the above section (in the following inversion chart LB).

Definition (LB = Left Bigger): Let σ ε S _{n be} a permutation and b _j with j = 1, 2, ..., n the number of elements to the left of j that are greater than j. Then I _lb (σ) = (b ₁ b ₂ ... b _n ) represents the inversion table LB of σ.

Definition (LS = Left Smaller): Let σ ε S _{n be} a permutation and b with j = 1, 2, ..., n the number of elements left of j that are smaller than j. Then I _ls (σ) = (b ₁ b ₂ ... b _n ) represents the inversion table LB of σ.

Definition (RB = Right Bigger): Let σ ε S _{n be} a permutation and b _j with j = 1, 2, ..., n the number of elements to the right of j that are greater than j. Then, I _rb (σ) = (b ₁ b ₂ ... b _n ) represents the inversion table LB of σ.

Definition (RS = Right Smaller): Let σ ε S _{n be} a permutation and b _j with j = 1, 2, ..., n the number of elements to the right of j which are smaller than j. Then I _rs (σ) = (b ₁ b ₂ ... b _n ) represents the inversion table LB of σ.

Example: By way of example, an example of the formation of an inversion table RS and the corresponding generation of the permutation is shown here.

First, take the element of permutation with σ (i) = 1 and count the elements to the right of σ (i) = 1 in σ which are smaller than 1. Here, this is not an element. Then take the element of permutation with σ (i) = 2 and count the smaller elements to the right of σ (i) = 1 in σ. Here, no element to the right of σ (i) = 2 is smaller than the second. If the same applies to | σ | Furthermore, I _rs (σ) = (b ₁ , ..., b4) = (0023). From an inversion table RS, j = 1, 2, ... | σ | generate the corresponding permutation again. For this, one goes the other way round and inserts j such that b _j elements to the right of it are smaller j. b1 = 0 1 b2 = 0 1 2 b3 = 2 3 1 2 b4 = 3 4 3 1 2

If one forms the inversion tables LB, LS and RB from σ, one obtains I lb (σ) = (2210) I ls (σ) = (0100) I lb (σ) = (1000)

A comparison of the entropies of the inversion tables from above shows that their entropies sometimes show considerable differences and in all cases are smaller than the entropy of the permutation (2 bits). HI lb (σ)) = 1.5 bits <2 bits = H (σ) HI ls (σ)) ≈ 0.81 bit <2 bit = H (σ) HI rb (σ)) ≈ 0.81 bit <2 bit = H (σ) HI rs (σ)) = 1.5 bits <2 bits = H (σ)

arnavut, Ziya: Permutation Techniques in Lossless Compression. Nebraska, University, Computer Science, Dissertation, 1995, pp. 58-78 in his dissertation several different methods of education used by inversion panels. However, he used other educational regulations for the Inversion tables. These are the Lehmer Inversion panels. If in the course of the speech of inversion panels, so are the meant non-Lehmer inversion panels. In the case of Lehmer inversion charts, the term "Lehmer" is explicitly stated. These should now be described and used in the further course.

Definition (Lehmer Inversion Board RS (Right Smaller)): Let σ ε S _{n be} a permutation. The Lehmer inversion _table RS I _rsl (σ) = (b1, b2, ..., b _n ) is then defined as b k = | {j: k <j ≤ n ∧ σ (k)> σ (j)} | for 1≤k≤n

• Algorithmus: 1 –1 / rsl(σ)
• 1. Setze i ← 1,1 ← (1, 2, ..., n)
• 2. σ(i) ← 1(b_i + 1)
• 3. 1 ← 1 – 1(b_i + 1) (entferne 1(b_i + 1) von 1)
• 4. i ← i + 1, falls i > n stop, andernfalls gehe zu 2.

The suffix rsl stands for "Right Smaller Lehmer". The same applies to the following definitions. Of course you can also generate the permutation from the Lehmer Inversion Board RS. In ARNAVUT, Ziya: Permutation Techniques in Lossless Compression. Nebraska, University, Computer Science, Dissertation, 1995 at pp. 62-63, the following algorithm has been given. Figure 1 illustrates a linked list in the algorithm

• Algorithm: 1 -1 / rsl (σ)
• 1. Set i ← 1.1 ← (1, 2, ..., n)
• 2. σ (i) ← 1 (b _i + 1)
• 3. 1 ← 1 - 1 (b _i + 1) (remove 1 (b _i + 1) from 1)
• 4. i ← i + 1, if i> n stop, otherwise go to 2.

arnavut, Ziya: Permutation Techniques in Lossless Compression. Nebraska, University, Computer Science, Dissertation, 1995 Although has in his Dissertation noted that he has several Lehmer inversion board education regulations However, no detailed definitions were used the remaining three Inversion Panel Formulation Rules (RBL, LSL and LBL) and equivalent Algorithms for recovery the permutation specified. Therefore, at this point, the corresponding Definitions and algorithms are given.

• Algorithmus: 1 –1 / rbl(σ)
• 1. Setzte i ← 1,1 ← (n, n – 1, ..., 1)
• 2. σ(i) ← 1(b_i + 1)
• 3. 1 ← 1 – 1(b_i + 1) (entferne 1(b_i + 1) von 1)
• 4. i ← i + 1, falls i > n stop, andernfalls gehe zu 2.

Definition (Lehmer Inversion Board RB). Let σ ε S _{n be} a permutation. The Lehmer inversion _table RB I _rbl (σ) = (b ₁ , b ₂ , ..., b _n ) is then defined as b k = | {j: k <j ≤ n ∧ σ (k) <σ (j)} | for 1≤k≤n.

• Algorithm: 1 -1 / rbl (σ)
• 1. Set i ← 1,1 ← (n, n-1, ..., 1)
• 2. σ (i) ← 1 (b _i + 1)
• 3. 1 ← 1 - 1 (b _i + 1) (remove 1 (b _i + 1) from 1)
• 4. i ← i + 1, if i> n stop, otherwise go to 2.

• Algorithmus: 1 –1 / lsl(σ)
• 1. Setzte i ← n, 1 ← (1, 2, ..., n)
• 2. σ(i) ← 1(b_i + 1)
• 3. 1 ← 1 – 1(b_i + 1) (entferne 1(b_i + 1) von 1)
• 4. i ← i – 1, falls i > n stop, andernfalls gehe zu 2.

Definition (Lehmer Inversion Board LS). Let σ ε S _{n be} a permutation. The Lehmer inversion _table LS I _lsl (σ) = (b ₁ , b ₂ , ..., b _n ) is then defined as b k = {j: j <k ≦ n ∧ σ (k)> σ (j)} | for 1≤k≤n

• Algorithm: 1 -1 / lsl (σ)
• 1. Set i ← n, 1 ← (1, 2, ..., n)
• 2. σ (i) ← 1 (b _i + 1)
• 3. 1 ← 1 - 1 (b _i + 1) (remove 1 (b _i + 1) from 1)
• 4. i ← i - 1, if i> n stop, otherwise go to 2.

• Algorithmus: 1 –1 / lbl(σ)
• 1. Setzte i ← n, 1 ← (n, n – 1, ...,1)
• 2. σ(i) ← 1(b_i + 1)
• 3. 1 4- 1 – 1(b_i + 1) (entferne 1(b_i + 1) von 1)
• 4. i ← i – 1, falls i > n stop, andernfalls gehe zu 2.

Definition (Lehmer Inversion panel LB). Let σ ε S _{n be} a permutation. The Lehmer inversion table LB 4.1 (σ) = (b ₁ , b ₂ , ..., b _n ) is then defined as b k = | {j: j <k ≦ n ∧ σ (k) <σ (j)} | for 1≤k≤n.

• Algorithm: 1 -1 / lbl (σ)
• 1. Set i ← n, 1 ← (n, n-1, ..., 1)
• 2. σ (i) ← 1 (b _i + 1)
• 3. 1 4-1 - 1 (b _i + 1) (remove 1 (b _i + 1) from 1)
• 4. i ← i - 1, if i> n stop, otherwise go to 2.

Example: Here, too, the construction of a Lehmer Inversion panel LB and the corresponding recovery of the permutation will be shown as an example for all four Lehmer inversion panels. Be given

First, take the first element of the permutation σ (1) = 4 and count the elements to the left of σ (1) in σ larger than 4. Here are 0 elements. Then take the second element of the permutation σ (2) = 3 and count the larger elements to the left of σ (2) in σ. Here is 1 element next to the σ (2) larger than the 3. If the same goes to 101 _Furthermore, I _lbl (σ) = (b ₁ , b ₂ , ..., b ₄ ) = (0122). From a Lehmer inversion table LB the corresponding permutation can be regenerated by algorithm I -1 / lbl (σ) l = (4, 3, 2, 1) b ₄ = 2 2 l = (4, 3, 1) b ₃ = 2 1 2 l = (4, 3). b ₂ = 1 3 1 2 l = (4) b ₄ = 0 4 3 2 1 l = {}

If one forms from σ the Lehmer Inverionstafeln RSL, RBL and LSL one receives 1 rsl (σ) = (3200) 1 rbl (σ) = (0010) , 1 lsl (σ) = (0001)

The property shown of the elements of the inversion panel LB also applies to the inversion panels RB, RBL and RSL. For the inversion panels LS, RS, LBL and LSL, however, the elements have the following properties 0 ≤ b i ≤ j - 1 (∀ j = 1, 2, ..., n).

Between the inversion tables and the Lehmer inversion tables, there is the following relation to entropy H (1 lb (σ)) = H (1 lbl (Σ)) H (1 ls (σ)) = H (1 lsl (Σ)) H (1 rb (σ)) = H (1 rbl (Σ)) H (l rs (σ)) = H (l rsl (Σ))

This is due to the fact that when forming the respective inversion table or Lehmer Inversion panel just the elements in a different order to be viewed as.

Around a statement about it how high the data rate is to encode a permutation will be now a measure for this Coding effort defined. For this measure will be the entropies of the different inversion tables or Lehmer inversion charts considered.

Definition (codability measure): Let σ be a permutation with | σ | <∞ and I _lb (σ), I _ts (u), I _ls (σ), I _rb (σ) are the corresponding inversion _tables or I _lbl (σ), I _lsl (σ), I _rbl (σ), I _rsl (σ) the corresponding Lehmer inversion tables, then the Codierbarkeitsmaß for permutations by C (σ) = min (H (1 lsl (σ)), H (1 lbl (σ)), H (1 rsl (σ)), H (1 rbl (σ))) = mm (H (l ls (σ)), H (1 lb (σ)), H (1 rs (σ)), H (1 rb (Σ))) Are defined.

Signaling which of the 8 inversion panel building codes was used can be done with 3 bits. Thus, using the best variant is more cost effective over ordinary binary coding of the permutation if the following inequality is for | σ | <∞ is true: 3 <(H (σ) - C (σ)) · | σ |.

• Algorithmus P (Shuffling): Sei X₁, X₂, ..., X_t eine Anzahl von t Zahlen die verwürfelt werden sollen
• P1. Initialisierung : Setze j ← t
• P2. Generiere U. Generiere eine Zufallszahl U zwischen 0 und 1 (gleichverteilt)
• P3. Vertauschung : Setze k ← ⌊jU⌋ + 1. Vertausche X_k ↔ X_j.
• P4. Verkleinere j : Verkleinere j um 1. Falls j < 1 gehe zu P2.

It has been determined by experimental investigations that for | σ | > 1 always H (σ)> C (σ) and as a result this inequality ab | σ | > 4 applies. This also answers the initial question as to whether a permutation can be coded with less than log ₂ (| σ |). For reasons of measurability, one is interested in scrambling permutations piece by piece starting from the identical permutation.

• Algorithm P (Shuffling): Let X ₁ , X ₂ , ..., X _{t be} a number of t numbers to be scrambled
• P1. Initialization: Set j ← t
• P2. Generate & generate a random number U between 0 and 1 (evenly distributed)
• P3. Exchange: Set k ← ⌊jU⌋ + 1. Swap X _k ↔ X _j .
• P4. Reduce j: Reduce j by 1. If j <1 go to P2.

The disadvantage of the algorithm is the choice of U. Depending on which U is chosen randomly, the t numbers in a transposition step are sometimes slightly more or sometimes less scrambled. However, the essential feature is the fact that the algorithm proceeds step by step and gradually increases the scrambling of an originally undiscussed permutation (identical permutation). Out 28 is clearly a property between length of the permutation, number of transpositions and the Kodierbarkeitsmaßes read out. 28 shows an illustration of the relationship between permutation length | s |, number of transpositions and codability measure. If the identical permutation is given, then the codability measure is 0. If only a few elements of the permutation are interchanged, the codability measure immediately increases very strongly. If more permutation elements are subsequently exchanged by transpositions, the curve flattens upward and runs counter to the empirically determined bit values from the following table | Σ | 128 192 256 320 384 448 512 576 640 704 768 832 896 960 1024 H (σ) 7:00 7:59 8:00 8:32 8:59 8.81 9:00 9.17 9:32 9:46 9:59 9.70 9.81 9.91 10:00 C (σ) 5.72 6:35 6.73 7:08 7:33 7:53 7.74 7.90 8:07 8.19 8:32 8:43 8:53 8.65 8.74

Now we want to show what form the inversion tables and Lehmer inversion tables of a permutation, which resulted from the sorting of the time values, have with different kind of music. For this a very tonal piece and a noisy piece is used. 29 shows a representation of inversion tables in the 10th block (frame) of a noise-like piece. 30 shows a representation of inversion tables in the 20th block (frame) of a tonal piece. It is based on a block size of 1024 time values.

In the 29 and 30 At first, the larger or smaller triangular waveform is striking. This waveform is conditioned by the underlying inversion panel formation rule and these equations. It is also noticeable that the Lehmer inversion panels both in the noise-like piece of music (see 29 ) as well as the tonal piece of music (see 30 ) are very uncorrelated. Whereas there is a clear difference between the tonal piece of music and the noisy piece of music in the inversion charts. If one considers the permutations belonging to the above inversion tables and Lehmer inversion tables, the permutation resulting from the sorting of the tonal piece of music is much more correlated there than that of the noisy piece of music (see 31 ). 31 FIG. 10 is an illustration of permutation of a noise-like piece resulting from a sorting of time values in FIG. 10. FIG. Block (left) and a tonal piece (right).

The right permutation off 31 is reminiscent of an audio signal mirrored on the main axis. It seems that there is a direct correlation between the audio signal, the sorting rule and even the inversion charts.

The 32 and 33 show the audio signal of a block, the corresponding permutation in which the x and y Koordina te has been swapped and the corresponding Inversionstafel LS. 32 shows on the left a part of an audio signal, the corresponding permutation and inversion table LS, and on the right the permutation and the inversion table LS from the left picture enlarged. 33 shows on the left a part of an audio signal, the corresponding permutation and inversion table LS, and on the right the permutation and the inversion table LS from the left picture enlarged.

The 32 and 33 clearly show the affinity of the original audio signal, permutation and inversion chart. Ie. As the amplitude of the original signal increases, so does the amplitude of the permutation and inversion chart, and vice versa. Very worth mentioning are the amplitude ratios. The maximum and minimum amplitude of the permutation always remains within a bounded framework of min (σ (i)) = 1 to max (σ (i)) = | σ |. The inversion table has even smaller amplitude values of min (σ (i)) -1 to max (σ (i)) -1 due to the above equations. In contrast, a 16-bit audio signal has a maximum amplitude range of-2ⁱ⁶ / 2 to 2ⁱ⁶ / 2 - 1. The principle just observed should now be emphasized explicitly.

principle the correlation transfer: The correlation of the audio signal is usually reflected in the sorted xy-swapped permutation and corresponding to the permutation corresponding Inversionstafel again. Because of the principle of correlation transfer shown above offers a prediction the inversion panels for further processing. For the prediction the described fixed predictor should be used. In general provides a prediction the Lehmer Inversion panels are not a good result. In very rare exceptions but it happens that the residual signal of the prediction of a Lehmer inversion board sometimes less bits needed as the residual signal of the inversion panels. Therefore, all 8 inversion panel formation prescriptions used. As a simplified MATLAB code, this can be done as in permCoding () represent.

Out It is known from the above section that the inversion tables are always one Have a shape that resembles a triangle. In rare cases can it happens that the prediction. the inversion charts and Lehmer inversion board is inefficient. To counter this problem, one can now use the triangular shape exploit the inversion panels and Lehmer inversion panels to create a Relatively inexpensive binary encoding to realize in the worst case case. The worst case case occurs z. For example, then when to encode noise-like or transient audio signals are. Because in these cases provides a prediction the inversion tables or Lehmer Inversionstafeln sometimes no good results. These are dependent on the respective Inversionstafelbildungsvorschrift always as much as necessary but as little as possible Bits for an ordinary one binary representation assigned to the elements. The corresponding dynamic bit allocation functions are as follows Are defined.

Definition (dynamic bit allocation function LS, RS, LBL, LSL). Let σ ε S _{n be} a permutation and b ₃ with j = 1, 2, ..., n be the elements of an inversion table formation rule, then the dynamic bit allocation function LS, RS, LBL, LSL be defined as

Definition (dynamic bit allocation function LB, RB, RBL, RSL). Let σ ε S _{n be} a permutation, and b with j = 1, 2, ..., n be the elements of an inversion chart, then the dynamic bit allocation function LB, RB, RBL, RSL defined as

The following table shows what this coding approach can do. | Σ | dynamic bit allocation static bit allocation 32 4,063 bits 5 bits 64 5,031 bits 6 bits 128 6,016 bits 7 bits 256 7,008 bits 8 bits 512 8,004 bits 9 bits 1024 9,002 bits 10 bits 2048 10,001 bits 11 bits

By one over the inversion panels and / or Lehmer inversion panels realized dynamic Bid allocation can be about 1 bit opposite an ordinary one binary encoding the permutation per element can be saved. This coding approach thus provides a simple and profitable approach for the worst case case.

In In this section we will investigate, as for the rest of the signals described decorrelation to entropy coding Shaping is as possible to achieve high compression. It was shown that the residual signal a prediction of approximate time values Laplace distribution has. This also applies to the residual signal of a prediction the non-Lehmer inversion boards.

Causal for that is the principle of correlation transfer described in the previous section.

34 FIG. 12 shows a probability distribution (top) and a length of the codewords (bottom) of a predicted (fixed predictor) residual signal of an inversion table LB. 34 shows the probability distribution of the residual signal of a non-Lehmer inversion chart LB, created by the application of a fixed predictor. For the determination of the code word lengths of the residual signal, a forward adaptive Rice coding with a parameter of k = 2 is used. It can be clearly seen that the probability distribution of the residual signal corresponds approximately to a Laplace distribution. In the case of a Laplace distribution, a Golomb or Rice coding is optimally suitable as entropy coding method.

Finally, the probability distribution of the residual signal of the difference coding of the sorted time values is still to be considered. 35 shows a probability distribution (top) and a length of codewords of a difference signal-generated residual signal (below) of sorted time values. In 35 It can clearly be seen that the residual signal has an approximately geometric probability distribution. Also in this case, a Golomb or Rice coding is very well suited as Entropiekodierverfahren. For the representation of the codeword lengths was in 35 used a forward-adaptive Rice coding with a parameter of k = 8.

In addition to the special probability distributions, the residual signals have the property that the value ranges from block to block sometimes vary considerably and many values of the value range do not occur at all. In 34 is this z. For example, between -25, ..., -20 the case. Also in 35 this can be seen for values> 350. A tabular storage of the codes or their transmission as page information, as z. B. would be the case with a Huffman coding is therefore unsuitable. Since each Rice or Golomb code is uniquely described by the parameter k or m, only k or m is to be transmitted as side information if a distinction is to be made between different Rice or Golomb codes. With the knowledge that a Rice or Golomb coding is perfectly suitable for the residual signals present in SOLO, different variants of a Rice or Golomb coding are to be developed.

• 1. vorwärts-adaptive Rice/Golomb Kodierung
• 2. rückwärts-adaptive Rice/Golomb Kodierung

Essential here is the determination of the Rice parameter k or the Golomb parameter m. Selecting the parameter too large increases the number of bits needed for the small numbers. If one chooses the parameter too small, the necessary number of bits for the unary coded part increases very strongly, especially for large values to be coded. A wrongly chosen parameter can thus the data rate of the entropy code increase significantly and thus worsen the compression. There are two ways to make a Rice or Golomb encoding:

• 1. forward-adaptive Rice / Golomb coding
• 2. backward-adaptive Rice / Golomb coding

mit zwei unterschiedlichen Bildungsvorschriften für den arithmetischen Mittelwert.Some methods to calculate the Rice parameter k forward-adaptively have already been shown. Further details of the forward-adaptive Rice parameter determination will now be explained. If there is a residual signal e (i) ∈ Z for i = 1, 2, ..., n, then first an M (e (i)) is made from Z to N ₀ . If the residual signal is already completely in N ₀ , as is the case with the residual signal of the difference coding of the sorted time values, then this mapping is omitted. The mapping from Z to No is assumed for e (i) ∈ Z in the following. Thus, the following equation results

with two different arithmetic mean training rules.

wobei ϕ = (√5 + 1)/2 ist.The easiest way to determine the Rice parameter is to test all the Rice parameters in question and choose the parameter with the lowest bit consumption. This is not very complex because the range of values of the Rice parameters to be tested is limited by the bit resolution of the time signal. At a resolution of 16 bits, a maximum of 16 Rice parameters must be verified. The corresponding bit requirement per parameter can ultimately be determined by means of a few bit operations or arithmetic operations. This procedure of finding the optimal Rice parameter is a bit more complicated than the direct calculation of the parameter, but always guarantees the optimal Rice parameter. In the lossless audio coding method presented here, in most cases this method is used to determine the Rice parameter. In a direct determination of the Rice parameter, the parameter limit values can be determined k min (μ) = max {0, ⌊log 2 | 2 3 (μ + 1)) ⌋} k Max (μ) = max {0, ⌊log 2 (Μ)} ⌋ to make use of. This will set the range of the optimal Rice parameter k k Max (μ) - k min (μ) ≤ 2 ∀μ limited and you have to test a maximum of 3 different Rice parameters to determine the optimal parameter. If there is a geometric probability distribution, then the optimal Rice parameter is given by the following equation

where φ = (√5 + 1) / 2.

In a forward-adaptive Golomb coding, a parameter determination using a search method, as was quite acceptable in the Rice coding, is much more complex. This is because the Golomb coding has significantly more intermediate gradations of the parameter m. Therefore, the Golomb parameter is calculated

berechnet.In this case, θ is going through

calculated.

With a forward-adaptive Rice / Golomb coding, it is possible to split a data block to be coded into several sub-blocks and to determine and transmit a separate parameter for each sub-block. As the number of subblocks increases, the necessary page information for the parameters increases. The effectiveness of the subblock decomposition strongly depends on how the parameters to be transmitted are coded themselves. Since the parameters of successive blocks usually do not vary very much, a difference coding of the parameters with subsequent forward-adaptive Rice coding is useful. If one now sums up the necessary data rate of the entropy-coded sub-blocks including the associated parameter page information over the entire block, and counts how often which sub-block dissection required the smallest data volume, the result for the entire coding process of a piece no 36 , 36 Figure 10 shows a percentage of a partial block decomposition with a least amount of data of a forward adaptive Rice coding over a residual signal of a fixed predictor of a piece including a side information for parameters, the total block length being 1024 time values. Number of subblocks 128 64 32 16 8th 4 2 1 Parameters uncoded 488 243 121 60 30 15 8th 4 Coded parameters 304 153 80 44 25 16 10 6 Sum of subblock data rates 9748 9796 9833 9872 9911 9926 9938 9952

For uncoded Rice parameters, a partial block decomposition is usually not very profitable. If the Rice parameters are coded, then a decomposition into 32 subblocks is often better than no subblock decomposition (see also the following table). In a forward-adaptive Golomb coding, a sub-block decomposition for both uncoded Golomb parameters and coded Golomb parameters is usually not advantageous (see 37 and the following table). 37 Figure 10 shows a percentage of a partial block decomposition with the lowest data volume of a forward adaptive Golomb coding over the residual signal of a fixed predictor of a piece including side information for parameters, the total block length being 1024 time values. However, it would be possible to quantize the Golomb parameters before encoding them, thereby reducing their necessary data rate. However, since the Rice parameters are in principle quantized Golomb parameters, this should not be considered here. Number of subblocks 128 64 32 16 8th 4 2 1 Parameters uncoded 1242 603 293 142 69 34 17 9 Coded parameters 1123 552 278 139 68 36 19 11 Sum of subblock data rates 9752 9794 9827 9863 9899 9913 9924 9938

• 1. Alle in Frage kommenden Teilblockzerlegungen zu testen und die mit der kleinsten Datenrate zu wählen.
• 2. Eine im Mittel gut geeignete Teilblockzerlegung für alle Fälle verwenden.

From the 36 and 37 It can be seen that there are no optimal partial block decompositions in all cases. Thus, there are two possibilities:

• 1. To test all possible sub-block decompositions and to select those with the smallest data rate.
• 2. Use an on average well-suited partial block decomposition for all cases.

Since the 1st possibility greatly increases the complexity of the system with slightly better compression, no partial block decomposition will be used in the further course. How to implement a forward-adaptive Rice or Golomb coding is shown in FwAdaptCoding (). At the beginning, a mapping to N0 takes place for a signed residual signal. This then determines the Rice / Golomb parameter and ultimately encodes all characters with this parameter. Here is a sample code

A backward-adaptive Rice / Golomb coding calculates the parameter from previously encoded characters. For this purpose, the newly encoded characters are entered cyclically in a history buffer. There are two variables to the history buffer. One holds the current level of the History Buffer and the other variable stores the next write position. In 38 the principle of operation of the size 8 History Buffer is shown.

wobei die Funktion l(e(i)) die nötige Anzahl der Bits für e(i) ermittelt, also

Initially, the history buffer is initialized to zero, the level is zero and the write index is one (see a)). Then one character at a time is entered in the history buffer and the writing index (arrows) and the filling level are updated (see b) -e)). Once the history buffer has been completely filled, the level remains constant (here 8) and only the writing index is adjusted (see e) -f)). The calculation of the backward adaptive Rice parameter is done as follows. Let e (i) ∈ N _{0 be} i = 1, 2, ..., W are the residual signal values contained in the history buffer, W is the size of the history buffer and F is the current level, then the backward adaptive Rice parameter is calculated by equation

where the function l (e (i)) determines the necessary number of bits for e (i), ie

The calculation of the backward-adaptive Golomb parameter is done by equation

By empirical experiments, C = 1.15 proved to be useful. For the size of the history buffer, a size of W = 16 is used in the following for both the backward adaptive Rice coding and the backward adaptive Golomb coding. This is a good compromise between too slow adaptation and overly responsive adaptation. As with backward adaptive arithmetic coding, the adaptation used for decoding must be synchronized for encoding, otherwise perfect reconstruction of the data is not possible. In some cases the reverse buffer does not yet have a good prediction of the parameter. Therefore, a variant is used which calculates a forward-adaptive parameter for the first W values, and only when the history buffer is completely filled, is this adaptive parameter calculated net.

How the adaptive parameter determination works is detailed in 39 shown. 39 shows an illustration of the operation of an adaptation compared with an optimal parameter for the entire block. The brighter lines represent the limit range from which the adaptive parameters are used. Simplified, this procedure can be described as in BwAdaptivCoding (). First, in the case of e (i) ∈ Z, another mapping to N ₀ follows. Then, via the first W values (size of the history buffer), a forward-adaptive parameter is determined with which the first W values are coded. If the history buffer is completely filled, the adaptive parameters are used for the further coding. Here is a sample code

In order to be able to assess the performance of the newly developed Rice / Golomb entropy coding methods more comprehensively, a forward adaptive arithmetic coding with the help of a backward adaptive Rice coding is to be developed in addition. First, a histogram of the data to be encoded is created. With this histogram it is possible to generate a code close to the entropy limit by the arithmetic coding. However, in addition, the contained characters and their occurrence probabilities must be transmitted. Since the characters in the histogram are arranged in a strictly monotonically increasing manner, a difference coding δ is available here before a backward-adaptive Rice coding. The probabilities are only encoded backwards-adaptive Rice. Ultimately, the total cost of doing this is given by the sum of the arithmetic coding code, the Rice coded characters, and the Rice coded probabilities (see 40 ). 40 shows an embodiment of a forward-adaptive arithmetic coding with the aid of a backward adaptive Rice coding.

Now the five different entropy coding methods will be compared. To this end, tables of all the residual signal signal generation methods present in the overall system are created, and the data volume is averaged per block over the entire piece in bytes. The following table shows a comparison of different entropy coding methods applied to the residual signal of the LPC predictor. Piece no. Entropy sums up especially Rice coding ra Rice coding especially Golomb coding ra Golomb coding especially Arith. Coding 1 1117 1242 1252 1241 1239 1599 2 1249 1980 1998 1981 1984 2548 4 910 988 974 985 960 1201 13 1026 1096 1111 1095 1098 1350 14 1111 1278 1291 1276 1279 1668

The following table shows a comparison of different entropy coding methods applied to the residual signal. Comparison of different entropy coding methods applied to the residual signal of the fixed predictor. Piece no. Entropy sums up especially Rice coding ra Rice coding especially Golomb coding ra Golomb coding especially Arith. Coding 1 1100 1243 1246 1241 1233 1599 2 1249 1982 1999 1983 1986 2543 4 908 1001 978 995 964 1218 13 989 1050 1111 1049 1052 1276 14 1140 1370 1381 1367 1370 1797

The following table shows a comparison of various entropy coding methods applied to the residual signal of a non-Lehmer inversion chart LB decorrelated with the fixed predictor Piece no. Entropy sums up especially Rice coding ra Rice _coding especially Golomb ^coding ra Golomb _coding especially Arith. Coding 1 674 705 677 698 665 780 2 1114 1241 1203 1237 1189 1603 4 683 767 764 755 721 833 13 659 687 670 680 656 754 14 856 922 907 914 883 1058

The following table shows a comparison of different entropy coding methods applied to the residual signal of the difference coding of the sorted time values Piece no. Entropy sums up especially Rice coding ra Rice _coding especially Golomb ^coding ra Golomb coding especially Arith. Coding 1 711 756 730 750 721 819 2 868 949 914 937 905 1051 4 471 547 487 528 476 540 13 610 660 624 653 615 694 14 605 678 622 665 613 697

If the rounded up arithmetic mean values are formed from the above tables, the following table results Entropy sums up 903 ra Golomb coding 1031 ra Rice coding 1045 especially Golomb coding 1052 especially Rice coding 1058 especially arithmetic coding 1282

For the final analysis the above table is still to be considered that the Golomb Parameter a little higher Page information data rate needed as the Rice parameter. Even so, the backward-adaptive Golomb introduces coding on average the best entropy coding method for the residual signals present in SOLO In very rare cases it may happen that the adaptation strategy fails and none gives good results. That is why SOLO is ultimately a combination from a backward-adaptive Golomb coding and a forward adaptive Rice coding used.

• • Wählt man die Blocklänge zu klein, so werden im Verhältnis zu den reinen Kodierungsdaten relativ viel Daten für die Seiteninformationen benötigt
• • Wählt man die Blocklänge zu groß, benötigt sowohl der Encoder als auch der Decoder große Datenstrukturen, um die zu bearbeitenden Daten im Speicher zu halten. Zudem stehen die ersten dekodierten Daten bei einer größeren Blocklänge auch erst später zur Verfügung als bei einer kleineren Blocklänge

In order to determine a suitable block size for an audio coding method, the following circumstances must always be taken into consideration:

• • If the block length is chosen too small, relatively much data is needed for the page information in relation to the pure coding data
• • If the block length is too large, both the encoder and the decoder require large data structures to hold the data to be processed in memory. In addition, the first decoded data are available with a larger block length also available later than with a smaller block length

in the essentially, therefore, the block length is determined by which Requirements for the coding process. Is that the Compression factor in the foreground, may be a very large block length acceptable. But is a coding with a low delay time or a small memory consumption demanded, so is a very size block length certainly not usable. Already existing audio coding method usually use block lengths from 128 to 4608 samples. At a sampling rate of 44.1 khz this corresponds to about 3 to 104 milliseconds. An investigation should Give information about how the different decorrelation methods used by SOLO at different block lengths behavior. These are different pieces at block lengths of 256, 512, 1024 and 2048 samples encoded and the compression factor F determined by inclusion of the respective page information. From The seven compression factors of a block length then become the arithmetic Mean value formed.

In 41 is the result of this investigation.

41 shows a representation of the influence of the block size on the compression factor F. It can be clearly seen that the predictors with increasing block length achieve a better compression factor, which is not so pronounced in the fixed predictor as in the LPC coding method. The sorting model decorrelation method has an optimum at a block length of 1024 samples. Since a high compression factor is desirable with as small a block length as possible, a block length of 1024 samples is primarily used in the following. However, SOLO can optionally be operated with a block length of 256, 512 or 2048 samples.

In The previous section has shown that a lossless stereo-redundancy reduction can be realized. One difficulty is that the middle channel M by a division with 2 followed by rounding to the nearest integer value with respect Zero has arisen. As a result, information has been lost in some cases. This is z. B. at L = 5, R = 4 of the case. We go in this example assume that there is only one value in each channel. In reality Of course, the left channel L or the right channel R are the same Vectors.

Here we get M = NINT ( L + R 2 ) = NINT ( 5 + 4 2 ) = NINT (4,5) = 4.

This information is still contained in the side channel S = L - R = 5 - 4 = 1. A lossy rounding of M has always occurred when S is odd. This must be taken into account when decoding. However, this just described possibility of correcting the center channel can be avoided if M is generated from R and S. S = L - R M = NINT ( S 2 ) + R

Graphically, the equation can be like in 42 represent. 42 shows a representation for lossless MS encoding. The MS decoding inverts the calculation rule of the MS encoding and generates from M and S again the right channel R and the left channel L R = M - NINT ( S 2 ) L = S + R

A graphical representation of the equation is in 43 shown. 43 shows a further illustration of the lossless MS encoding.

• 1. LR-Kodierung: keine Stereoredundanzreduktion
• 2. LS-Kodierung: linker Kanal und Seitenkanal
• 3. RS-Kodierung: rechter Kanal und Seitenkanal
• 4. MS-Kodierung: Mittenkanal und Seitenkanal

In addition to MS coding, LSO and RS coding for stereo-redundancy reduction should also be used within SOLO. Thus there are a total of four variants for the coding of stereo signals:

• 1. LR coding: no stereo redundancy reduction
• 2. LS coding: left channel and side channel
• 3. RS coding: right channel and side channel
• 4. MS coding: center channel and side channel

As but should one decide which coding is best? A possibility would it be to develop a criterion which is the variant with the smallest Selects data traffic before getting the decorrelation and entropy coding of each Channels performs. This possibility needed significantly less memory and is only half as complex as the procedure described below. However, the hangs Goodness decisively from the decision criterion. You could use entropy (Equation 2.3) use. However, experiments have shown that entropy therefor not a reliable decision criterion represents.

Another possibility would be to process L, R, M and S completely, and to decide which bit variant to use according to the bit consumption. Here you need more memory and computing time, but can certainly always select the cheapest option. In the following, only the second option is used (s. 44 ). 44 shows an illustration to select a best variant for stereo reduction reduction.

A study will now show what this procedure does for stereo signals. The following table compares the average entropy over the entire piece of the different variants. A block length of 1024 time values per channel was used throughout. In the last column (best variant), the mean entropy of the procedure is 44 shown. Piece no. L R S M LR LS RS MS Best variant 16 (L = R) 9.64 9.64 0 9.64 19:28 9.64 9.64 9.64 9.64 17 9.64 9.62 9:55 9.63 19:26 19:19 19:17 19:18 19:16 18 8.74 8.77 7.62 8.74 17:51 16:36 16:39 16:36 16:34 19 7.79 7.84 4:32 7.83 15.63 12:11 12:16 12:15 12:10 20 8.29 8.30 5:07 8.30 16:59 13:36 13:37 13:37 13:35 27 9.18 9.18 9.23 9.11 18:36 18:41 18:41 18:34 18:32 28 9:36 9:38 9:41 9:33 18.74 18.77 18.79 18.74 18.72 29 9.12 9.10 9.15 9:07 18:22 18:27 18:25 18:22 18:20

The most profitable is the procedure after 44 for stereo signals with identical channels. For strongly monophonic pieces of speech, how does the presented stereo-redundancy reduction benefit much, whereas for normal pieces of music such as 17, 27, 28 and 29, only a very small coding gain is achieved between the LR-coding and the selection of the best variant.

Especially It is noted that depending on the circumstances the inventive concept can also be implemented in software. The implementation can on a digital storage medium, in particular a floppy disk or a CD with electronically readable control signals, the so with a programmable computer system and / or microcontroller can work together that the corresponding procedure is carried out. Generally exists The invention thus also in a computer program product with a on a machine-readable carrier stored program code for carrying out the method according to the invention, if the computer program product is on a computer and / or microcontroller expires. In other words Thus, the invention can be considered as a computer program with a program code to carry out the process can be realized when the computer program is up a computer and / or microcontroller expires.

Claims (70)

Contraption ( 100 ) for encoding a sequence of samples of an audio signal, each sample within the sequence having an origin position, comprising: means ( 110 ) for sorting the samples by size to obtain a sorted sequence of samples, each sample having a sorting position within the sorted sequence; and a facility ( 120 ) for encoding the sorted samples and information about a relationship between the source and sort positions of the samples, the device ( 120 ) is adapted to code to determine and encode coefficients of a prediction filter based on a permutation or an inversion table. Contraption ( 100 ) according to claim 1, further comprising preprocessing means configured to perform filtering, time / frequency transformation, prediction or multi-channel redundancy reduction for generating the sequence of samples. Contraption ( 100 ) according to one of claims 1 or 2, in which the device ( 120 ) is adapted to code to encode the information about the relationship between the source and sort positions as an index permutation. Contraption ( 100 ) according to one of claims 1 to 3, in which the device ( 120 ) is adapted to code to encode the information about the relationship between the originating and sorting positions as an inversion chart. Contraption ( 100 ) according to one of claims 1 to 4, in which the device ( 120 ) is adapted to code to encode the sorted samples or the information on the relationship between the source and sort positions with difference and subsequent entropy coding or only entropy coding. Contraption ( 100 ) according to one of claims 1 to 5, in which the device ( 120 ) is adapted to be coded to determine and to code coefficients of a prediction filter based on the sorted samples. Contraption ( 100 ) according to claim 6, wherein the device ( 120 ) for coding to code a residual signal corresponding to a difference between the samples and an output of the prediction filter. Contraption ( 100 ) according to claim 7, wherein the device ( 120 ) is adapted to code to encode the residual signal with an entropy coding. Contraption ( 100 ) according to one of claims 1 to 8, further comprising means for setting functional coefficients of a functional rule for adapting the functional specification to at least a portion of the sorted sequence, and wherein the device ( 120 ) is adapted to code to code the function coefficients. Method for coding a sequence of samples an audio signal, each sample within the sequence has an originating position, with the following steps: sort by the samples according to their size, by one assorted sequence of samples, each sample has a sorting position within the sorted sequence; and Encoding the sorted samples and information about the Relationship between the origin and sorting positions of the Samples based on coefficients of a prediction filter of a permutation or an inversion board. Computer program with a program code for executing the Process according to claim 10, when the computer program runs on a computer. Contraption ( 150 ) for decoding a sequence of samples of an audio signal, each sample within the sequence having an origin position, comprising: means ( 160 ) for receiving a sequence of encoded samples, each encoded sample having a sorting position within the sequence of encoded samples, and for receiving information about a relationship between the source and sort positions of the samples; a facility ( 170 ) for decoding the samples and the information about the relationship between the original and sort positions based on coded coefficients of a prediction filter to determine a permutation or an inversion table; and a facility ( 180 ) for resorting the samples based on the information on the relationship between the source and sort positions so that each sample has its origin position. Contraption ( 150 ) according to claim 12, wherein the device ( 160 ) is adapted to receive the information about the relationship between the source and sort positions as an index permutation. Contraption ( 150 ) according to claim 13, in which the device ( 160 ) for receiving to receive the information about the relationship between the originating and sorting positions as the inversion chart. Contraption ( 150 ) according to one of claims 12 to 14, in which the device ( 170 ) for decoding to decode the coded samples or the information on the relationship between the original and sort positions with an entropy and then difference decoding or only a de-copy decoding. Contraption ( 150 ) according to one of claims 12 to 15, in which the device ( 160 ) is adapted to receive coded coefficients of a prediction filter and the device ( 170 ) for decoding to decode the coded coefficients, the device ( 150 ) further comprises means for predicting samples based on the coefficients. Contraption ( 150 ) according to claim 16, in which the device ( 160 ) is adapted to receive further to receive a residual signal corresponding to a difference between the samples and an output of the prediction filter, and the means ( 170 ) is further adapted for decoding to adjust the samples based on the residual signal. Contraption ( 150 ) according to claim 17, wherein the device ( 170 ) is adapted for decoding to decode the residual signal with entropy decoding. Contraption ( 150 ) according to one of claims 12 to 18, in which the device ( 160 ) for receiving is further adapted to receive functional coefficients of a functional specification and wherein the device ( 150 ) further comprises means for adapting a functional rule to at least a portion of the sorted sequence and the device ( 170 ) is adapted for decoding to decode the function coefficients. Method of decoding a sequence of samples an audio signal, each sample within the sequence has an originating position, with the following steps: Receive a sequence of coded samples, each coded sample within the sequence of coded samples, a sorting position having; Receiving information about a relationship between the source and sort positions of the samples; Decode the samples and the information about the relationship between the source and sort positions based on coded Coefficients of a prediction filter for determining a permutation or inversion panel; and rearrange the samples based on the information about the relationship between the source and sort positions so that each sample has its original position. Computer program with a program code for executing the The method of claim 20, when the program code is on a computer accomplished becomes. Contraption ( 200 ) for encoding a sequence of samples of an information signal, each sample within the sequence having an origin position, comprising: means ( 210 ) for sorting the samples by size to obtain a sorted sequence of samples, each sample having a sorting position within the sorted sequence; a facility ( 220 ) for setting function coefficients of a functional specification for adapting the functional specification to a subarea of the sorted sequence; and a facility ( 230 ) for encoding the function coefficients, the samples outside the subarea, and information about a relationship between the origin and sort positions of the samples. Contraption ( 200 ) according to claim 22, further comprising preprocessing means configured to filter, time / frequency transform, predict or multichannel danzreduktion to generate the sequence of samples to perform. Contraption ( 200 ) according to one of claims 22 or 23, wherein the information signal comprises an audio signal. Contraption ( 200 ) according to one of claims 22 to 24, in which the device ( 230 ) is adapted to code to encode the information about the relationship between the source and sort positions as an index permutation. Contraption ( 200 ) according to one of claims 22 to 25, in which the device ( 230 ) is adapted to code to encode the information about the relationship between the originating and sorting positions as an inversion chart. Contraption ( 200 ) according to one of claims 22 to 26, in which the device ( 220 ) is adapted to code to encode the sorted samples, the information on the relationship between the source and sort positions with difference and subsequent entropy coding or only entropy coding. Contraption ( 200 ) according to one of claims 22 to 27, in which the device ( 230 ) is adapted to code to determine and encode coefficients of a prediction filter based on the samples, a permutation or an inversion table. Contraption ( 200 ) according to claim 28, wherein the device ( 230 ) for encoding is further configured to encode a residual signal corresponding to a difference between the samples and an output of a prediction filter. Contraption ( 200 ) according to claim 29, wherein the device ( 230 ) is adapted to code to encode the residual signal with an entropy coding. Method for coding a sequence of samples an information signal, each sample within the Sequence has an origin position, with the following steps: sort by the samples according to their size, by one assorted sequence of samples, each sample has a sorting position within the sorted sequence; To adjust of function coefficients of a function rule for adaptation the functional specification to a subarea of the sorted sequence; and coding the function coefficients, the samples outside of the subarea and information about a relationship between the source and sort positions of the samples. Computer program with a program code for carrying out the Process according to claim 31, when the program code is executed on a computer. Contraption ( 250 ) for decoding a sequence of samples of an information signal, each sample within the sequence having an origin position, comprising: means ( 260 ) for receiving coded function coefficients, sorted samples and information about a relationship between a sort position and the origin position of samples; a facility ( 270 ) for decoding samples; a facility ( 280 ) for approximating samples based on the function coefficients in a portion of the sequence; and a facility ( 290 ) for reordering the samples and the subarea based on the information about the relationship between the source and sort positions so that each sample has its origin position. Contraption ( 250 ) according to claim 33, wherein the information signal comprises an audio signal. Contraption ( 250 ) according to one of claims 33 or 34, in which the device ( 260 ) is adapted to receive the information about the relationship between the source and sort positions as an index permutation. Contraption ( 250 ) according to one of claims 33 to 35, in which the device ( 260 ) to receive is designed to receive the information about the relationship between the original and sorting positions as an inversion table. Contraption ( 250 ) according to one of claims 33 to 36, in which the device ( 270 ) is further adapted to decode the function coefficients, the sorted samples or the information about the relationship between the original and sorting positions with an entropy and subsequent difference decoding or only an entropy decoding. Contraption ( 250 ) according to one of claims 33 to 37, wherein the device ( 260 ) is adapted to receive coded coefficients of a prediction filter and the device ( 270 ) for decoding to decode the coded coefficients, the device ( 250 ) further comprises means for predicting samples based on the coefficients. Contraption ( 250 ) according to one of claims 33 to 38, in which the device ( 260 ) is adapted to receive a residual signal representing a difference between the samples and an output signal of the prediction filter or the device ( 280 ) to approximate, to receive and the device ( 270 ) is adapted for decoding to adjust the samples based on the residual signal. Contraption ( 250 ) according to claim 39, wherein the device ( 270 ) is adapted to decode to decode the residual signal with an entropy decoding. Method of decoding a sequence of samples an information signal, each sample within the Sequence has an origin position, with the following steps: Receive coded function coefficients, sorted samples and an information about a relationship between a sorting position and the originating position of samples; Decoding samples; approximate of samples based on the function coefficients in one Subregion of the sequence; and Resorting to the samples and of the subarea based on the information about the relationship between the source and sort positions so that each sample has its original position. Computer program with a program code for carrying out the Process according to claim 41, when the program code is executed on a computer. Contraption ( 300 ) for encoding a sequence of samples of an information signal, each sample within the sequence having an origin position, comprising: means ( 310 ) for sorting the samples by size to obtain a sorted sequence of samples, each sample having a sorting position within the sorted sequence; a facility ( 320 ) for generating a sequence of numbers depending on a relationship between the original and sort positions of the samples and for determining coefficients of a prediction filter based on the sequence of numbers; and a facility ( 330 ) for encoding the sorted samples and the coefficients. Contraption ( 300 ) according to claim 43, further comprising preprocessing means configured to perform filtering, time / frequency transform, prediction or multi-channel redundancy reduction to generate the sequence of samples. Contraption ( 300 ) according to one of claims 43 or 44, wherein the information signal comprises an audio signal. Contraption ( 300 ) according to one of claims 43 to 45, in which the device ( 320 ) is configured to generate the sequence of numbers to produce an index permutation. Contraption ( 300 ) according to one of claims 43 to 46, in which the device ( 320 ) for generating the sequence of numbers is formed to produce an inversion panel. Contraption ( 300 ) according to one of claims 43 to 47, in which the device ( 320 ) for generating the sequence of numbers for further generating a residual signal corresponding to a difference between the sequence of numbers and a prediction order predicted on the basis of the coefficients. Contraption ( 300 ) according to one of claims 43 to 48, in which the device ( 330 ) is adapted for coding to encode the sorted samples or the coefficients according to difference or entropy coding. Contraption ( 300 ) according to one of claims 48 or 49, in which the device ( 330 ) for encoding is further adapted to code the residual signal. Method for coding a sequence of samples an information signal, each sample within the Sequence has an origin position, with the following steps: sort by the samples according to their size, by one assorted sequence of samples, each sample has a sorting position within the sorted sequence; Produce dependent on a sequence of numbers a relationship between the source and sort items sampling and determining coefficients of a prediction filter based on the sequence of numbers; and Encoding the sorted ones Samples and the coefficients. Computer program with a program code for carrying out the Process according to claim 51, when the program code is executed on a computer. Contraption ( 350 ) for decoding a sequence of samples of an information signal, each sample within the sequence having an origin position, comprising: means ( 360 ) for receiving coefficients of a prediction filter and a sequence of samples, each sample having a sort position; a facility ( 370 ) for predicting a sequence of numbers based on the coefficients; and a facility ( 380 ) for reordering the sequence of samples based on the sequence of numbers such that each sample has its original position. Contraption ( 350 ) according to claim 53, wherein the information signal comprises an audio signal. Contraption ( 350 ) according to one of claims 53 or 54, in which the device ( 370 ) predicates an index permutation as a sequence of numbers to predict the sequence of numbers. Contraption ( 350 ) according to one of claims 53 to 55, in which the device ( 370 ) predicts an inversion chart as a sequence of numbers to predict the sequence of numbers. Contraption ( 350 ) according to one of claims 53 to 56, in which the device ( 360 ) for receiving is further adapted to receive a coded residual signal and the device ( 370 ) is designed for prediction to take into account the residual signal in the prediction of the sequence of numbers. Contraption ( 350 ) according to one of claims 53 to 57, further comprising means for decoding configured to decode samples, residual signals or coefficients after difference or entropy coding. Method of decoding a sequence of samples an information signal, each sample within the Sequence has an origin position, with the following steps: Receive of coefficients of a prediction filter and a sequence of samples, each sample one Has sorting position; Predicting a sequence of numbers based on the coefficients; and Resorting to the sequence of samples based on the sequence of numbers so that each sample has its original position. Computer program with a program code for carrying out the Process according to claim 59, when the program code is executed on a computer. Contraption ( 400 ) for encoding a sequence of samples, each sample within the sequence having an origin position, comprising: means ( 410 ) for sorting the samples by size to obtain a sorted sequence of samples, each sample having a sorting position within the sorted sequence; and a facility ( 420 ) for encoding the sorted samples and encoding a sequence of numbers with a Information about the relationship between the original and sorting positions of the samples, each element unique within the sequence of numbers, and wherein the device ( 420 ) assigns a number of bits to an element of the number sequence such that the number of bits allocated to a first element is greater than the number of bits allocated to a second element if prior to the coding of the first element fewer elements were already coded than before the coding of the second element. Contraption ( 400 ) according to claim 61, wherein the device ( 420 ) is adapted to code to encode a number sequence of length N and to encode a number of X elements simultaneously, the number of X elements being assigned to G bits according to,

Contraption ( 400 ) according to claim 61, wherein the device ( 420 ) is adapted to code to encode a number sequence of length N, where X is a number of already encoded elements of the. Number sequence is where the next element of the sequence of numbers G bits are assigned according to, G = ⌈log 2 (N - X) ⌉ with 0 ≤ X <N. Method for coding a sequence of N samples, wherein each sample within the sequence has an origin position, with the following steps: Sort the samples according to theirs Size to one assorted sequence of samples, each sample has a sorting position within the sorted sequence; Encode the sorted samples; and Coding a sequence of numbers with information about the relationship between the source and sort items the samples, each element unique within the sequence of numbers is, and wherein the coding of an element of the sequence of numbers a Number of bits, such that the number of bits, that is assigned to a first element is greater than the number of Bits assigned to a second element if before coding of the first element fewer elements were already encoded than before the coding of the second element. Computer program with a program code for carrying out the Process according to claim 64, if the program code is run on a computer. Contraption ( 450 ) for decoding a sequence of samples, each sample within the sequence having an origin position, comprising: means ( 460 ) for receiving a coded sequence of numbers and a sequence of samples, each sample having a sorting position; a facility ( 470 ) for decoding a decoded number sequence with information about a relationship between the original and sort positions based on the encoded sequence of numbers, each element unique within the decoded sequence of numbers, and the device ( 470 ) for decoding assigns a number of bits to an element of the sequence of numbers such that the number of bits allocated to a first element is greater than the number of bits allocated to a second element if prior to the decoding of the first element fewer elements were already decoded than before the encoding of the second element; and a facility ( 480 ) for reordering the sequence of samples based on the decoded number sequence so that each sample within the decoded sequence has its original position. Contraption ( 450 ) according to claim 66, wherein the device ( 470 ) is adapted to decode a number sequence of length N and to simultaneously decode a number of X elements, wherein the number of X elements are assigned to G bits according to,

Contraption ( 450 ) according to claim 66, wherein the device ( 470 ) is adapted for decoding to decode a sequence of numbers of length N, where X is a number of already encoded elements of the sequence of numbers, where the next element of the sequence of numbers G bits are assigned according to, G = ⌈log 2 (N - X) ⌉ with 0 ≤ X <N. Method of decoding a sequence of samples, wherein each sample within the sequence is an origin position comprising, with the following steps: Receiving a coded Number sequence and a sequence of samples, each sample has a sorting position; Decoding the encoded Number sequence with information about a relationship between the source and sort positions based on the coded one Number sequence, where each element within the decoded number sequence is unique and when decoding an element of the sequence of numbers is assigned a number of bits such that the number of bits Bits allocated to a first element is larger as the number of bits allocated to a second element if fewer elements already exist before decoding the first element were decoded as before the coding of the second element; and rearrange the sequence of samples based on the decoded sequence of numbers, such that each sample within the decoded sequence is its Has original position. Computer program with a program code for carrying out the Process according to claim 69, when the program code is executed on a computer.